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  • Blackwell Publishing Ltd  (1,089)
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  • Articles  (1,089)
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  • 1
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    Oxford, UK : Blackwell Publishing Ltd
    Journal of the American Ceramic Society 80 (1997), S. 0 
    ISSN: 1551-2916
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: X-ray diffraction (XRD) patterns from nominally β-SiC specimens often differ from those expected for the cubic crystal structure. These differences include the presence of additional peaks, enhanced background intensities, peak broadening, changes in relative peak heights, and shifts in peak positions. It has long been recognized that they are due to the presence of stacking faults, and models relating the experimental observations to stacking fault population have continued to evolve. The presence and relative magnitude of these features vary among different β-SiC specimens. In this work, computer simulations were used to show that the variations are closely related to differences in the type and spatial distribution of stacking faults in each specimen. In these simulations, stacking sequences were generated using a selectively activated 1-D Ising model with a Boltzmann-type probability function for specifying errors, which allows a wide variety of fault configurations to be generated. Direct correlations between different features in the XRD data to the underlying fault population are demonstrated, which are discussed in this paper. It is also shown that this computer model is general, in the sense that many of the models presented in prior work can be interpreted as limiting cases of it.
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  • 2
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    Mathematical finance 6 (1996), S. 0 
    ISSN: 1467-9965
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics , Economics
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  • 3
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    Oxford, UK : Blackwell Publishing Ltd
    Teaching statistics 6 (1984), S. 0 
    ISSN: 1467-9639
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics
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  • 4
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    Mathematical finance 6 (1996), S. 0 
    ISSN: 1467-9965
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics , Economics
    Notes: Barrier options have become increasingly popular over the last few years. Less expensive than standard options, they may provide the appropriate hedge in a number of risk management strategies. In the case of a single-barrier option, the valuation problem is not very difficult (see Merton 1973 and Goldman, Sosin, and Gatto 1979). the situation where the option gets knocked out when the underlying instrument hits either of two well-defined boundaries is less straightforward. Kunitomo and Ikeda (1992) provide a pricing formula expressed as the sum of an infinite series whose convergence is studied through numerical procedures and suggested to be rapid. We follow a methodology which proved quite successful in the case of Asian options (see Geman and Yor 1992,1993) and which has its roots in some fundamental properties of Brownian motion. This methodology permits the derivation of a simple expression of the Laplace transform of the double-barrir price with respect to its maturity date. the inversion of the Laplace transform using techniques developed by Geman and Eydeland (1995), is then fairly easy to perform.
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  • 5
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    Oxford, UK : Blackwell Publishing Ltd
    Mathematical finance 6 (1996), S. 0 
    ISSN: 1467-9965
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics , Economics
    Notes: In markets where dealers play a central role, bid-ask spreads inhibit asset valuation as defined by the formation cost of a replicating portfolio. We introduce a nonlinear valuation formula similar to the usual expectation with respect to the risk-adjusted probability measure. This formula expresses the asset's selling and buying prices set by dealers as the Choquet integrals of their random payoffs We investigate several price puzzles: the violation of the put-call parity and the fact that the components of a security can sell at a premium to the underlying security (primes and scores).
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  • 6
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    Mathematical finance 6 (1996), S. 0 
    ISSN: 1467-9965
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics , Economics
    Notes: In the stochastic volatility framework of Hull and White (1987), we characterize the so-called Black and Scholes implied volatility as a function of two arguments the ratio of the strike to the underlying asset price and the instantaneous value of the volatility By studying the variation m the first argument, we show that the usual hedging methods, through the Black and Scholes model, lead to an underhedged (resp. overhedged) position for in-the-money (resp out-of the-money) options, and a perfect partial hedged position for at the-money options These results are shown to be closely related to the smile effect, which is proved to be a natural consequence of the stochastic volatility feature the deterministic dependence of the implied volatility on the underlying volatility process suggests the use of implied volatility data for the estimation of the parameters of interest A statistical procedure of filtering (of the latent volatility process) and estimation (of its parameters) is shown to be strongly consistent and asymptotically normal.
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  • 7
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    Oxford, UK : Blackwell Publishing Ltd
    Mathematical finance 6 (1996), S. 0 
    ISSN: 1467-9965
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics , Economics
    Notes: In this paper we address existence of equilibria in an incomplete markets economy with countably many periods and a continuum of states at each node of the infinite tree. We consider two models: one where agents have to honor their commitments and another where default is allowed. In both models, marginal utility of income, at each node, is shown to be bounded, and we prove existence by taking finite-dimensional approximations and applying Fatou's lemma sequentially.
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  • 8
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    Mathematical finance 6 (1996), S. 0 
    ISSN: 1467-9965
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics , Economics
    Notes: This paper addresses the problem of estimating and analyzing the residual risk that is not hedged by a discrete hedging strategy. the use of die chaotic representation allows an elegant decomposition of the residual risk to be hedged by adequate assets. Alternative strategies to the classical delta hedging and optimization under the risk-neutral and historical probabilities are discussed.
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  • 9
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    Mathematical finance 6 (1996), S. 0 
    ISSN: 1467-9965
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics , Economics
    Notes: We consider the problem of pricing path-dependent contingent claims. Classically, this problem can be cast into the Black-Scholes valuation framework through inclusion of the path-dependent variables into the state space. This leads to solving a degenerate advection-diffusion partial differential equation (PDE). We first estabilish necessary and sufficient conditions under which degenerate diffusions can be reduced to lower-dimensional nondegenerate diffusions. We apply these results to path-dependent options. Then, we describe a new numerical technique, called forward shooting grid (FSG) method, that efficiently copes with degenerate diffusion PDEs. Finally, we show that the FSG method is unconditionally stable and convergent. the FSG method is the first capable of dealing with the early exercise condition of American options. Several numerical examples are presented and discussed./〉
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  • 10
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    Mathematical finance 6 (1996), S. 0 
    ISSN: 1467-9965
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics , Economics
    Notes: The extended Cox-Ingersoll-Ross (ECIR) models of interest rates allow for time-dependent parameters in the CIR square-root model. This article presents closed-form pathwise unique solutions of these unsolved stochastic differential equations (s.d.e.s) in terms of functionals of their driving Brownian motion and parameters. It is shown that quadratics in solution of linear s.d.e.s solve the ECIR model if and only if the dimension of the model is a positive integer and that this solution can be achieved by construction of a pathwise unique generalized Ornstein-Uhlenbeck process from the ECIR Brownian motion. For real valued dimensions an extension of the time-change theorem of Dubins and Schwarz (1965) is presented and applied to show that a lognormal process solves the model through a stochastic time change. Pathwise equivalence to a rescaled time-changed Bessel square process is also established. These novel results are applied to characterize zero-hitting time and to produce transition density and zero-hitting conditions for the ECIR spot rate. the CIR term structure is then extended to ECIR under no arbitrage, and its solutions and the transition density are represented under a new ECIR martingale measure. the findings are employed to derive a closed-form ECIR bond option valuation formula which generalizes that obtained by CIR (1985).
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  • 11
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    Mathematical finance 5 (1995), S. 0 
    ISSN: 1467-9965
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics , Economics
    Notes: We investigate an optimal consumption/investment decision problem with partially observable drift. Logarithmic utilities are shown to be necessary and sufficient for the certainty equivalence principle to hold. For the sufficiency part of the proof, we allow a general stochastic structure about the unobservable drift. On the other hand, a simple Bayesian structure is assumed for the necessity part in order to utilize the Hamilton-Jacobi-Bellman equations.
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  • 12
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    Mathematical finance 5 (1995), S. 0 
    ISSN: 1467-9965
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics , Economics
    Notes: Book Review in this Articleeconomic and financial modelling with mathematica, hal R. varian (editor), telos/springer-verlag. new york 1993
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  • 13
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    Mathematical finance 5 (1995), S. 0 
    ISSN: 1467-9965
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics , Economics
    Notes: This paper uses the existence of secondary markets for debt instruments with default risk (e.g. corporate bonds) to define default insurance along the lines of financial economics. It examines whether, in the case of several risk-neutral measures, characteristics of default can be uniquely determined by the prices of contracts involving default-prone securities.
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  • 14
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    Mathematical finance 5 (1995), S. 0 
    ISSN: 1467-9965
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics , Economics
    Notes: We derive a necessary and sufficient condition for the existence of a nonnegative equilibrium price vector under which the total demand and supply of each asset balances in the standard mean-variance capital market. Also, we give an explicit formula for such a price vector. This formula shows that the price of assets is an increasing function of p̄, the weighted average of the requested rate of return of individual investors, which tends to infinity as p̄ approaches the expected rate of return on the market portfolio. Further, we construct a macroeconomic index which gives information about the soundness of the capital market.
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  • 15
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    Mathematical finance 5 (1995), S. 0 
    ISSN: 1467-9965
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics , Economics
    Notes: It is shown how, even when the market is incomplete, certain contingent claims are attainable: that is, they can be represented as stochastic integrals with respect to the process which describes the evolution of the asset prices.
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  • 16
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    Mathematical finance 5 (1995), S. 0 
    ISSN: 1467-9965
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics , Economics
    Notes: This paper introduces new techniques for modeling financial data under the assumption that the data belong to the domain of attraction of a multivariate stable Pareto law. We provide tail estimators for the index of stability parameter a and the corresponding spectral measure. These estimators are then applied to test the associtation of the individual components and to compute estimates of portfolio risk and the covariation of commodities. A practical example is given using DM-dollar and JY-dollar exchange rates data.
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  • 17
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    Mathematical finance 5 (1995), S. 0 
    ISSN: 1467-9965
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics , Economics
    Notes: Book Review in this Article Dynamic Asset Pricing Theory, By Darrell Duffie
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  • 18
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    Mathematical finance 6 (1996), S. 0 
    ISSN: 1467-9965
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics , Economics
    Notes: Stochastic dominance (SD) is a very useful tool in various areas of economics and finance. the purpose of this paper is to provide the results of SD relations developed in other areas such as applied probability which, we believe, are useful for many portfolio selection problems. In particular, the bivariate characterization of SD relations given by Shanthikumar and Yao (1991) is a powerful tool for the demand and the shift effect problems in optimal portfolios. the method enables one to extend many results that hold for the case where the underlying lying assets are statistically independent to the dependent case directly.
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  • 19
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    Mathematical finance 6 (1996), S. 0 
    ISSN: 1467-9965
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics , Economics
    Notes: We study the pricing of American options on two stocks without expiration date and with payoff functions which are positively homogeneous with respect to the two stock prices. Examples of such options are the perpetuai Margrabe option, whose payoff is the amount by which one stock outperforms the other, and the perpetual maximum option, whose payoff is the maximum of the two stock prices Our approach to pricing such options is to take advantage of their stationary nature and apply the optional sampling theorem to two martingales constructed with respect to the risk-neutral measure the optimal exercise boundaries, which do not vary with respect to the time variable, are determined by the smooth pasting or high contact condition the martingale approach avoids the use of differential equations.
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  • 20
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    Mathematical finance 6 (1996), S. 0 
    ISSN: 1467-9965
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics , Economics
    Notes: We derive a formula for the minimal initial wealth needed to hedge an arbitrary contingent claim in a continuous-time model with proportional transaction costs; the expression obtained can be interpreted as the supremum of expected discounted values of the claim, over all (pairs of) probability measures under which the “wealth process” is a supermartingale. Next, we prove the existence of an optimal solution to the portfolio optimization problem of maximizing utility from terminal wealth in the same model, we also characterize this solution via a transformation to a hedging problem: the optimal portfolio is the one that hedges the inverse of marginal utility evaluated at the shadow state-price density solving the corresponding dual problem, if such exists. We can then use the optimal shadow state-price density for pricing contingent claims in this market. the mathematical tools are those of continuous-time martingales, convex analysis, functional analysis, and duality theory.
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  • 21
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    Mathematical finance 6 (1996), S. 0 
    ISSN: 1467-9965
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics , Economics
    Notes: In a stochastic volatility model, the no-free-lunch assumption does not induce a unique arbitrage price because of market incompleteness. In this paper, we consider a contingent claim on the primitive asset, traded in zero net supply. Given a system of Arrow-Debreu state prices, we provide necessary and sufficient conditions for consistency with an intertemporal additive equilibrium model that we fully characterize. We show that the risk premia corresponding to the minimal martingale of Föllmer and Schweizer (1991) are consistent with logarithmic preferences, while the Hull and White model (1987) (volatility risk premium independent of the asset price) is consistent with a class of utility functions including constant relative risk aversion (CRRA) ones.
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  • 22
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    Mathematical finance 6 (1996), S. 0 
    ISSN: 1467-9965
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics , Economics
    Notes: This paper introduces a method for constructing option hedging strategies in the presence of transaction costs. the approach begins with the prescription of a large, but tractable class of strategies. A variational problem is constructed in which the expected square replication error is minimized subject to a fixed initial portfolio value from among the class of strategies. the solution of this variational problem results in a replicating strategy which simulations show outperforms strategies previously considered. We illustrate this method in a particular class of strategies which contains Leland's discrete time replication scheme. We show that a strategy which uses varying time intervals between hedging can significantly reduce replication error for a given initial wealth. We will also construct and assess strategies obtained by optimizing a mean-variance criterion. This methodology extends to other optimization problems involving initial portfolio value and expected square replication error, as well as to other classes of strategies.
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  • 23
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    Mathematical finance 6 (1996), S. 0 
    ISSN: 1467-9965
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics , Economics
    Notes: This paper presents a consistent and arbitrage-free multifactor model of the term structure of interest rates in which yields at selected fixed maturities follow a parametric muitivariate Markov diffusion process with “stochastic volatility.” the yield of any zero-coupon bond is taken to be a maturity-dependent affine combination of the selected “basis” set of yields. We provide necessary and sufficient conditions on the stochastic model for this affine representation. We include numerical techniques for solving the model, as well as numerical techniques for calculating the prices of term-structure derivative prices. the case of jump diffusions is also considered.
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  • 24
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    Mathematical finance 6 (1996), S. 0 
    ISSN: 1467-9965
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics , Economics
    Notes: We consider a pure exchange economy consisting of a single risky asset whose dividend drift rate is modeled as an Omstein-Uhlenbeck process, and a representative agent with power-utility who, in equilibrium, consumes the dividend paid by the risky asset. Endogenously determined interest rates are found to be of the Vasicek (1977) type the mean and variance of the equilibrium stock price are stochastic and have mean-reverting components A closed-form solution for a standard call option is determined for the case of log-utility. Equilibrium values have interesting implications for the equity premium puzzle observed by Mehra and Prescott (1985)
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  • 25
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    Mathematical finance 5 (1995), S. 0 
    ISSN: 1467-9965
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics , Economics
    Notes: For general volatility structures for forward rates, the evolution of interest rates may not be Markovian and the entire path may be necessary to capture the dynamics of the term structure. This article identifies conditions on the volatility structure of forward rates that permit the dynamics of the term structure to be represented by a two-dimensional state variable Markov process. the permissible set of volatility structures that accomplishes this goal is shown to be quite large and includes many stochastic structures. In general, analytical characterization of the terminal distributions of the two state variables is unlikely, and numerical procedures are required to value claims. Efficient simulation algorithms using control variates are developed to price claims against the term structure.
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  • 26
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    Mathematical finance 5 (1995), S. 0 
    ISSN: 1467-9965
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics , Economics
    Notes: This paper demonstrates the use of term-structure-related securities in the design of dynamic portfolio management strategies that hedge certain systematic jump risks in asset return. Option pricing formulas based on the absence of arbitrage opportunities in this context are also developed. the analysis is for the case where assets returns are driven by a finite number of Brownian motions and an m-variate point process. the inclusion of :the additional traded assets in the term structure makes it possible to hedge systematic jumps imbedded in the m variate point process.
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  • 27
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    Mathematical finance 6 (1996), S. 0 
    ISSN: 1467-9965
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics , Economics
    Notes: The general equilibrium model with incomplete markets is here extended to infinite horizon economies populated by a finite number of infinitely lived agents. the crucial issue that divides the infinite horizon setting from the finite horizon setting is in the nature of borrowing constraints, which added to spot constraints, define a plausible budget set for individual agents. the paper relates seven alternative definitions of equilibrium and states corresponding equilibrium existence theorems when assets are one-period and purely financial.
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  • 28
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    Mathematical finance 6 (1996), S. 0 
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    Topics: Mathematics , Economics
    Notes: Ross (1976) has shown, in a static framework, how options can complete financial markets. This paper examines the possible extensions of Ross's idea in a dynamic setup. Surprisingly enough, we find that the answer is very sensitive to the choice of the stochastic model for the underlying security returns. More specifically we obtain the following results: In a discrete-time model, classical European options typically become redundant with some probability (Proposition 2.1). Obnly path dependent (“exotic”) options may generate dynamic spanning (Proposition 4.1). In a continuous-time model with stochastic volatility of the underlying security, and under reasonable assumptions, a European option is always a good instrument for completing markets (Proposition 5.2).
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  • 29
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    Mathematical finance 6 (1996), S. 0 
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    Topics: Mathematics , Economics
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  • 30
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    Mathematical finance 5 (1995), S. 0 
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    Topics: Mathematics , Economics
    Notes: We consider the problem of a trustee faced with investing a sum of money, the interest from which will be received by one party (the life-tenant) during his lifetime while the capital will go to another party (the survivor) on the death of the life-tenant. We assume mat there are n+ 1 assets in which the trustee may invest—n risky assets of geometric Brownian motion type and one nonrisky asset. Under assumptions as to the utility functions of the two parties, we find the collection of Pareto optimal investment strategies for the trustee together with the corresponding payoffs. We do this by optimizing the payoff of the Lagrangian for the problem. We go on to present the Nash optimal solution for the trustee.
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  • 31
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    Mathematical finance 5 (1995), S. 0 
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    Topics: Mathematics , Economics
    Notes: We study optimal portfolio management policies for an investor who must pay a transaction cost equal to a fixed Traction of his portfolio value each time he trades. We focus on the infinite horizon objective function of maximizing the asymptotic growth rate, so me optimal policies we derive approximate those of an investor with logarithmic utility at a distant horizon. When investment opportunities are modeled as m correlated geometric Brownian motion stocks and a riskless bond, we show that the optimal policy reduces to solving a single stopping time problem. When there is a single risky stock, we give a system of equations whose solution determines the optima! rule. We use numerical methods to solve for the optima! policy when there are two risky stocks. We study several specific examples and observe the general qualitative result that, even with very low transaction cost levels, the optimal policy entails very infrequent trading.
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  • 32
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    Mathematical finance 5 (1995), S. 0 
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    Topics: Mathematics , Economics
    Notes: We examine the Morton and Pliska (1993) model for the optimal management of a portfolio when there are transaction costs proportional to a fixed fraction of the portfolio value. We analyze this model in the realistic case of small transaction costs by conducting a perturbation analysis about the no-transaction-cost solution. Although the full problem is a free-boundary diffusion problem in as many dimensions as there are assets in the portfolio, we find explicit solutions for the optimal trading policy in this limit. This makes the solution for a realistically large number of assets a practical possibility.
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    Mathematical finance 5 (1995), S. 0 
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    Topics: Mathematics , Economics
    Notes: In this paper we derive the implications of the absence of arbitrage in securities markets models where traded securities are subject to short-sales constraints and where the borrowing and lending rates differ. We show that a securities price system is arbitrage free if and only if there exists a numeraire and an equivalent probability measure for which the normalized (by the numeraire) price processes of traded securities are supermartingales. Also, the tightest arbitrage bounds that can be inferred on the price of a contingent claim without knowing agents’preferences are equal to its largest and smallest expected normalized payoff with respect to the supermartingale measures. In the case where the underlying security price follows a diffusion process and where short selling is possible but costly, we derive partial differential equations that must be satisfied by the arbitrage bounds on derivative securities prices, and we determine optimal hedging strategies. We compute the arbitrage bounds on common securities numerically for several values of the borrowing and short-selling costs and show that they can be quite sharp.
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    Mathematical finance 5 (1995), S. 0 
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    Topics: Mathematics , Economics
    Notes: We study the critical price of an American put option near expiration in the Black-Scholes model. Our main result is an estimate for the difference P̄ (t)- K between the critical price at time t and the exercise price as t approaches the maturity of the option.
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    Topics: Mathematics , Economics
    Notes: A common theme in the literature on corporate control is that, when share ownership is diffuse, the free-rider problem prevents raiders from making acquisitions at tender prices below the postacquisition share price. In this paper, we address this question by formulating a nonstandard model of takeovers of diffusely held firms. It is demonstrated that, even when individual shareholdings are infinitesimal relative to firm size, takeovers succeed with positive probability and equilibria exist in which the raider earns substantial per share profits. Further, the Nash equilibria of the game are characterized with regard to raider profit, the aggregate fraction of shares tendered, and the relation between raider profit and the degree of randomization exhibited by shareholder tendering strategies.
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    Mathematical finance 5 (1995), S. 0 
    ISSN: 1467-9965
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics , Economics
    Notes: Many embedded options are difficult to value the wild card option in the Treasury bond futures contract is one of these embedded options. We illustrate how narrow theoretical bounds on the value of this option, relative to the price of the contract, may be obtained in the presence of other embedded options. Simulations suggest that the value of the wild card option is close to zero. This implies that, in this economy, a simpler pricing model of the Treasury bond futures contract, which ignores the wild card option, will result in only a small loss of accuracy.
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    Mathematical finance 5 (1995), S. 0 
    ISSN: 1467-9965
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics , Economics
    Notes: The value of a future cash stream is often taken to be its net present value with respect to some term structure. This means that a linear formula is used in which each future payment is discounted by a factor deemed appropriate for the date on which the payment will be made. In a money market with taxes and shorting costs, however, there is no theoretical support for the existence of a universal term structure for this purpose. What is worse, reliance on linear formulas can be seriously inaccurate relative to true worth and can lead to paradoxes of disequilibrium. A consistent no-arbitrage theory of valuation in such a market requires instead that taxed and untaxed investors be grouped in separate classes with different valuation operators. Such operators are linear to scale but nonlinear with respect to addition. Here it is established that although these valuation operators provide general bounds applicable across an entire class, individual investors within a tax class can have more special operators because of the influence of existing holdings. These customized valuation operators have the feature of not even being linear to scale. In consequence of this nonlinearity, investors from the same or different tax classes can undertake advantageous trades even when the market is in a no-arbitrage state, but such trade opportunities are limited. Some degree of activity in financial markets can thereby be understood without appeal to differences in utility functions or temporary disequilibrium due to random disturbances.
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    Mathematical finance 5 (1995), S. 0 
    ISSN: 1467-9965
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics , Economics
    Notes: We consider a two-country economy under the nonarbitrage assumption and where volatilities are stochastic. Assuming the existence of state variables, we show that, under some mild volatility assumptions, the model is actually fully specified. In particular, both term structure dynamics and the exchange rate process can be given endogeneously under the risk-neutral probability. We then derive the exact dependence of the zero-coupon bonds and the exchange rate on the underlying state variables. As a result, some closed-form solutions can be proposed for the derivative assets as futures and options written on foreign zero-coupon bonds.
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    Mathematical finance 5 (1995), S. 0 
    ISSN: 1467-9965
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics , Economics
    Notes: This article develops an option pricing model and its corresponding delta formula in the context of the generalized autoregressive conditional heteroskedastic (GARCH) asset return process. the development utilizes the locally risk-neutral valuation relationship (LRNVR). the LRNVR is shown to hold under certain combinations of preference and distribution assumptions. the GARCH option pricing model is capable of reflecting the changes in the conditional volatility of the underlying asset in a parsimonious manner. Numerical analyses suggest that the GARCH model may be able to explain some well-documented systematic biases associated with the Black-Scholes model.
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    Mathematical finance 5 (1995), S. 0 
    ISSN: 1467-9965
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics , Economics
    Notes: This paper augments the theoretical foundations of organized commodity futures markets and uncovers singular facts about arbitrage and the role of information. Using the term “credit agency” to embrace organized futures markets such as the Chicago Board of Trade as well as independent brokerage houses, we extend the extant theory of temporary equilibrium for an economy with a single credit agency to economies with many credit agencies. In the process, we find that arbitrage with no risk of bankruptcy and with perfect interagency trade information can be incompatible with equilibrium (exact or approximate). On the other hand, the usual regularity assumptions are sufficient for the existence of at least an approximate equilibrium, provided that interagency trade information is imperfect (or risky). However, such imperfect information limits arbitrage so different agencies can have different prices.
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  • 41
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    Fatigue & fracture of engineering materials & structures 20 (1997), S. 0 
    ISSN: 1460-2695
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract— This paper examines the application of the Jk, L and M integrals, in complex-variable form, to the Boussinesq wedge. The wedge is symmetrical and subjected to a point couple and point forces at the apex of the wedge. In the case of a point couple acting at the wedge apex the Jy, L and M integrals are found to vanish for all wedge angles whereas Jx displays a 1/r3 path-dependence; where r is a radial dimension measured from the wedge apex. When the wedge is subjected to point forces at the wedge apex then Jx and Jy are 1/r path-dependent whereas L and M are path-independent.The property that the L and M integrals are path-independent for the Boussinesq wedge is applied to the problem of determining the modes I and II stress intensity factors for a corner-loaded edge crack in a half-plane subjected to both normal and parallel point forces to the free surface of the half-plane.
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  • 42
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    Fatigue & fracture of engineering materials & structures 20 (1997), S. 0 
    ISSN: 1460-2695
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract— Fatigue tests were performed on thin-walled tubular specimens of S45C steel under tension-compression, pure torsion, in-phase and out-of-phase axial-torsional loadings. The relationship between cracking behaviour and stress components on the crack plane was investigated. Measurement of microcrack density showed that microcracking was governed predominantly by the shear stress amplitude acting on the crack plane for all loading conditions. The failure crack was formed by coalescence of many cracks initiated near the maximum shear planes. The cracks grew turning their orientation to the direction perpendicular to the maximum normal stress. The transition of crack orientation occurred at relatively longer crack lengths at a higher stress ratio. The crack growth behaviour for all loading modes can be correlated using an equivalent strain intensity parameter based on shear and normal strains on the crack plane.
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  • 43
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    Fatigue & fracture of engineering materials & structures 20 (1997), S. 0 
    ISSN: 1460-2695
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract— A ductile medium strength steel has been modelled by means of the Gurson model, and been used to investigate the effect of crack tip constraint in several fracture mechanics specimens. Both numerical and experimental results have been obtained, in the course of the crack extension process, for single edge notch bending specimens with different crack length-to-width ratios. The geometries with the shorter cracks always exhibited higher J values at initiation and steeper J crack growth resistance curves, and these results have been explained in terms of the stress and strain fields and damage development in the region ahead of the crack tip.
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    Fatigue & fracture of engineering materials & structures 20 (1997), S. 0 
    ISSN: 1460-2695
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract— It is shown that autofrettage at low temperatures is superior to autofrettage at room temperature in enhancing the fatigue resistance of thick-walled tubes against pulsating internal pressure. The physical reason is based on the well-known temperature dependence of the mechanical behaviour of metals and alloys which generally exhibit an enhancement of both the yield stress and strain hardening behaviour at lower temperatures. As a consequence, significantly larger compressive residual hoop stresses can be introduced during pressurization at low temperatures than at room temperature. Experimental data obtained on thick-walled tubes of the metastable austenitic stainless steel AISI 304 L which were subjected to pulsating internal pressure at room temperature after autofrettage at temperatures between-110°C and room temperature are presented. These data demonstrate convincingly the advantages offered by low-temperature autofrettage in enhancing both the fatigue life in the finite-life region and the fatigue endurance limit in comparison with autofrettage at room temperature. In conclusion, some specific materials requirements for optimum low-temperature autofrettage performance are discussed.
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  • 45
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    Fatigue & fracture of engineering materials & structures 20 (1997), S. 0 
    ISSN: 1460-2695
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract— A new single-specimen testing method, the normalization method with the so-called LMN calibration function, based on the load separation principle and function calibrations from an individual test record, was used to construct J-R curves directly from load versus load-line displacement records without any additional on-line crack-length monitoring equipment. The research was done on CT-specimens of a glassy polymer PVC at different crosshead speeds ranging from 0.01 to 50 mm/min. The J-R curves evaluated from the normalization method are in good agreement with those from the conventional multiple-specimen testing method in the whole range of the tested crosshead speeds. The results demonstrated the applicability of the normalization method for developing J-R curves at different crosshead speeds in PVC. The crack initiation J-integral values, J0.2, showed a two-regime dependence on the crosshead speeds in the tested crosshead speed range.
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  • 46
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    Fatigue & fracture of engineering materials & structures 20 (1997), S. 0 
    ISSN: 1460-2695
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract— Biaxial fatigue tests were conducted on a high strength spring steel using hour-glass shaped smooth specimens. Four types of loading system were employed, i.e. (a) fully reversed cyclic torsion, (b) uniaxial push—pull, (c) fully reversed torsion with a superimposed axial static tension or compression stress, and (d) uniaxial push—pull with a superimposed static torque, to evaluate the effects of mean stress on the cyclic stress—strain response and short fatigue crack growth behaviour. Experimental results indicate that a biaxial mean stress has no apparent influence on the stress—strain response in torsion, however a superimposed tensile mean stress was detrimental to torsional fatigue strength. Similarly a superimposed static shear stress reduced the push—pull fatigue lifetime. A compressive mean stress was seen to be beneficial to torsion fatigue life. The role of mean stress on fatigue lifetime, under mixed mode loading, was investigated through experimental observations and theoretical analyses of short crack initiation and propagation. Using a plastic replication technique the effects of biaxial mean stress on both Stage I (mode II) and Stage II (mode I) short cracks were evaluated and analysed in detail. A two stage biaxial short fatigue crack growth model incorporating the influence of mean stress was subsequently developed and applied to correlate data of crack growth rate and fatigue life.
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    Fatigue & fracture of engineering materials & structures 20 (1997), S. 0 
    ISSN: 1460-2695
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract— The development of fatigue damage in Co45Ni specimens during push—pull and reversed torsion tests, performed inside a scanning electron microscope, was observed and the different stress states compared. It appeared that transgranular crack initiation and development is delayed and intergranular crack initiation promoted under torsional loading. This was explained in terms of reduced surface distortion at the emergence of persistent slip bands (PSBs) and smaller compatibility stresses at the PSB-matrix interfaces. The influence of the mechanical strength of grain boundaries on the difference between tensile and torsional fatigue lives is discussed.
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    Fatigue & fracture of engineering materials & structures 20 (1997), S. 0 
    ISSN: 1460-2695
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    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract— A Fourier series approach is proposed to calculate stress intensity factors using weight functions for semi-elliptical surface cracks in flat plates subjected to two-dimensional stress distributions. The weight functions were derived from reference stress intensity factors obtained by three-dimensional finite element analyses. The close form weight functions derived are suitable for the calculation of stress intensity factors for semi-elliptical surface cracks in flat plates under two-dimensional stress distributions with the crack aspect ratio in the range of 0.1 ≤a/c≤ 1 and relative depth in the range of 0 ≤a/t≤ 0.8. Solutions were verified using several two-dimensional non-linear stress distributions; the maximum difference being 6%.
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    Fatigue & fracture of engineering materials & structures 20 (1997), S. 0 
    ISSN: 1460-2695
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract— A conventional finite element method may show a weakness when determining the hot spot stress distributions in the brace/chord intersection region of offshore tubular joints. This is because the chosen element displacement functions do not implicitly satisfy the conditions which prevail on the free surfaces. A procedure has been proposed to modify the conventional finite element method so as to allow the hot spot stresses, which occur at the free boundary of the weld toe of tubular joints, to be determined with improved accuracy. The results obtained by this modified method are compared with both an experimental and a traditional finite element solution. The comparison shows that the modified solution is in better agreement with the experimental data as compared with the traditional solution.
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    Fatigue & fracture of engineering materials & structures 20 (1997), S. 0 
    ISSN: 1460-2695
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    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
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    Fatigue & fracture of engineering materials & structures 20 (1997), S. 0 
    ISSN: 1460-2695
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    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract— Simple extensions to the standard deep notch bend test procedure are suggested to allow the collection of data relevant to the energy dissipation rate, D, crack opening angle, COA, and J, all for arbitrarily large amounts of growth in extensive plasticity. The methods of analysis are detailed for real elastic-plastic behaviour of a high strength low-hardening type metal with a view to encouraging use on a wider range of materials. A proposal is made, and equations given, that the particular version of J used for an R-curve derived from the area under the loading diagram, should correspond to the value of the far-field integral, Jff.The relationship between the global measure of COA that emerges from D and the local crack tip opening angle, CTOA, as used in computational studies, is established. Transferability of CTOA data is examined in the light of effects of size and configuration. An explicit rule of the form CTOA √G =f (material and configuration) is proposed for the modelling of ductile growth in finite element studies. It is applied to a set of data in the literature, for the variation of CTOA with size in the deep notch bend test and for the configurations, bending, double edge and centre cracked tension.
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    Fatigue & fracture of engineering materials & structures 20 (1997), S. 0 
    ISSN: 1460-2695
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    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract— In this investigation the Electron Channelling Contrast (ECC) technique in scanning electron microscopy (SEM) was applied to reveal the dislocation structures in the vicinity of surface fatigue cracks in comparison to those of cyclically-deformed recrystallized polycrystalline copper. The plastic zone around a fatigue crack was found to consist of an innermost region containing cells, followed by a region containing dense veins and PSBs, surrounded by a structure of loose veins, bundles and loop patches typical of the cyclically deformed matrix. A relation between plastic strain amplitude values deduced from cyclic stress-strain investigations and the dislocation structures near fatigue cracks are given. Typical regions of damage accumulation were identified and plastic strain contours for surface fatigue cracks established. The essentially non-destructive ECC technique is particularly suited to identify the changes in mesoscopic dislocation structures from surface layers to the interior of specimens over large specimen areas.
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    Fatigue & fracture of engineering materials & structures 20 (1997), S. 0 
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    Fatigue & fracture of engineering materials & structures 20 (1997), S. 0 
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    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract— The propagation behaviour of fatigue cracks emanating from pre-cracks was numerically simulated to evaluate the development of crack closure with crack growth. The crack opening stress intensity factor at the threshold was approximated as a function of the applied stress and the amount of crack extension. Pre-cracked specimens of a medium-carbon steel with a small surface crack and a single-edge crack were fatigued to investigate experimentally the initiation and propagation of cracks from pre-cracks. Crack closure was dynamically measured by using an interferometric strain/displacement gauge. The threshold condition of crack initiation from pre-cracks was given by a constant value of the effective stress intensity range which was equal to the threshold value for long cracks. The cyclic R-curve was constructed in terms of the threshold value of the maximum stress intensity factor as a function of crack extension approximated on the basis of the experimental and numerical results. The cyclic R-curve method was used to predict the fatigue thresholds of pre-cracked specimens. The predicted values of the fatigue limits for crack initiation and fracture, and the length of non-propagating cracks agreed very well with the experimental results.
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    Fatigue & fracture of engineering materials & structures 20 (1997), S. 0 
    ISSN: 1460-2695
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    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract— A basic study was performed on the evolution of three-dimensional shapes of small surface fatigue cracks during fatigue, and the effect of this evolution on small-crack growth behavior of a titanium-base alloy. Specifically, the nature and the magnitude of variations in crack aspect ratio, a/c (a is the crack depth and c is the half-surface crack length), during cyclic crack growth and its impact on growth rates have been studied. Experiments were performed on naturally initiated micro-cracks in a microstructure consisting of equiaxed primary-α2 phase in a Widmanstätten (transformed β) matrix. Several cracks under stress ratio (R) levels of 0.1 and −1, were studied. A specialized experimental system, consisting of a laser interferometer (to measure precisely the small-crack surface displacements), and a photo microscope (to automatically and continuously photograph the fatigue micro-cracks) was employed in the study. Apparent aspect ratios of surface cracks were calculated from the compliance response and the surface crack length data as a function of fatigue cycles. These data enabled accurate calculations of growth rates at the surface crack tip as well as the tip at depth in the bulk over the entire crack growth period, thus giving an insight into the crack growth process. Measurements of closure levels of small cracks were also performed and were used to partly account for the differences in growth rates. In the comparisons of small-crack growth data with the large-crack data, surface growth rates correlated relatively well with the large-crack data. Growth rates at depth exhibited large variations due to the irregularity of crack fronts at this location, and these rates deviated significantly from the large-crack behavior. Additionally, these growth rates varied between different cracks. An attempt was made to rationalize these observations in terms of the effects of inhomogeneities present in the microstructure.
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    Fatigue & fracture of engineering materials & structures 20 (1997), S. 0 
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    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract— A new technique, known as crack modelling, is used here to predict fatigue failure in a crankshaft component. The technique uses a linear elastic finite element (FE) analysis to derive a stress intensity factor (K) for the component under load. The novel feature of the technique is that K is calculated without introducing a crack into a component; the stress field around the maximum stress point is examined and compared to that for a standard centre-cracked plate. The fatigue limit for a crankshaft was successfully predicted, when compared to experimental data. The only material parameter required for this prediction was the threshold stress intensity range, ΔKth.
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    Fatigue & fracture of engineering materials & structures 20 (1997), S. 0 
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    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract— The effects of bluing, associated with drawing strain, on the fatigue strength of eutectoid steel wires have been investigated. The fatigue limit increases by bluing and the increase is more significant with higher drawing strain. The peak in the fatigue limit with regard to the drawing strain in the wires, at a strain of 2.5, disappears after bluing. On the other hand, in the ferritic steel wires investigated for comparison, the fatigue limit gradually increases with the drawing strain up to 7.7. Furthermore, no appreciable change in the fatigue limit due to bluing is found. Based on the results of hardness tests on fatigue specimens with- and without-bluing, it is deduced that the decrease of the fatigue limit beyond the peak drawing strain in the eutectoid steel wire can partly be attributed to insufficient locking of the high-density dislocations by solute atoms. The effect of relaxation of residual stress during bluing is also briefly discussed.
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    Fatigue & fracture of engineering materials & structures 20 (1997), S. 0 
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    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract— It is well known that for very short cracks the stress intensity factor K is not a suitable parameter to estimate the stress level over the small but finite Stage II process zone activation region of size rs near the crack tip, within which crack growth events take place. A critical appreciation of the reasons for the limitations on the applicability of ΔK as a fatigue crack propagation (FCP) parameter, when the crack length a is of the same order of magnitude or smaller than the size of the ‘fatigue-fracture activation region’, rs is presented. As an alternative to ΔK the range Δσs of the cyclic normal stress at a point situated at the fixed distance s=rs/2, ahead of the crack tip, inside the fatigue-fracture activation region, is proposed. It is observed that the limitation on the use of ΔK when the crack is short, is mathematical (and not physical) but this inconvenience is easily circumvented if the stress Δσs at the prescribed distance is used instead of ΔK since nowadays Δσs can be obtained numerically by using finite element methods (FEM). It follows that the parameter Δσs is not restricted by the mathematical limitations on ΔK and so it would seem that there is, a priori, no reason why the validity of the parameter Δσs cannot be extended to short cracks. It is shown that if the Paris law is expressed in terms of Δσs (πrrs)½ instead of ΔK the validity of the modified Paris law can be extended to short cracks.A coherent estimate of the value of the fatigue-fracture activation region rs is derived in terms of the fatigue limit ΔσFL obtained from S-N tests and of the threshold value ΔKth obtained from tests on long cracks where both relate to Stage II crack growth that ends in failure, namely, rs= (ΔKth/ΔσFL)2/π. An overall, threshold diagram is presented based on the simple criterion that, for sustained Stage II FCP, Δσs must be greater than ΔσFL. The study is based on a simple continuum mechanics approach and its purpose is the investigation of the suitability of both ΔK and Δσs to characterise the crack driving force that activates complex fracture processes at the microstructure's scale. The investigation pertains to conditions that lead to the ultimate failure of the component at values of Δσs 〉 ΔσFL.
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    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract— The boundary value problem for an arbitrarily shaped plane crack embedded in a 3D linear elastic solid can be reduced to a governing hyper-singular integral equation. A discretizing procedure based on a triangulation of the crack area has been offered in Part I of this work. The main goal of Part I is to introduce the analytical results for the 18 resulting finite-part integrals defined over a triangular mesh area. The finite-part integrals occur in those triangles where the source point coincides with one of the element nodes. Mostly the source point lies outside of the considered triangle. In these cases the occurring area integrals are regular.The aim of Part II is, therefore, the derivation of the closed form expressions for the relevant 18 regular area integrals. The resulting relations are of algebraic form which can easily be coded in compact form. Their numerical proof by two different methods shows the highest accuracy and, therefore, the correctness of the final solutions. The relevant numerical results are offered in Appendix I.With the formulae provided in Part I and Part II of the paper the determination of the coefficient matrix, necessary for the calculation of COD values from a linear equation system, is precise and needs only minimum computer time.
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    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract— Circumferentially notched cylindrical specimens are tested in torsion to obtain critical J values from crack resistance curves. The specimens are explosion cladded, half ferrite, half austenite, with the interface perpendicular to the cylinder axis and the circumferential notch at, or parallel to, the interface. Critical J values for crack extension in mode III were found to be a factor 1.1 to 2.1 higher than under comparable mode I loading.
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    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract— Strength measurements are becoming increasingly important for electroceramics. Bending of specimens small enough to be cut out of small electroceramic components may be one possibility. Therefore the miniaturisation of the 4-point bend-test for ceramic specimens is now being attempted. In this paper the errors in determining the flexural strength arising from the test principle itself, plus the geometry and measuring inaccuracies are calculated and expressed as a function of the outer span length. Contact pressure and a tolerable total measuring inaccuracy determines the dimensions of miniature specimens and fixtures. The possibilities of appropriate specimen preparation are also investigated.Ceramic materials show a volume (i.e. a specimen size) dependence of strength which is described by Weibull's statistical theory. The applicability of the miniature bend-fixtures is demonstrated by measuring this volume effect.
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    Fatigue & fracture of engineering materials & structures 20 (1997), S. 0 
    ISSN: 1460-2695
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    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract— This paper describes a versatile technique for simulating the fatigue growth of a wide range of planar cracks of practical significance. Crack growth is predicted on a step-by-step basis from the Paris law using stress intensity factors calculated by the finite element method. The crack front is defined by a cubic spline curve from a set of nodes. Both the 1/4-node crack opening displacement and the three-dimensional J-integral (energy release rate) methods are used to calculate the stress intensity factors. Automatic remeshing of the finite element model to a new position which defines the new crack front enables the crack propagation to be followed. The accuracy and capability of this finite element simulation technique are demonstrated in this paper by the investigation of various problems of both theoretical and practical interest. These include the shape growth trend of an embedded initially penny-shaped defect and an embedded initially elliptical defect in an infinite body, the growth of a semi-elliptical surface crack in a finite thickness plate under tension and bending, the propagation of an internal crack in a round bar and the shape change of an external surface crack in a pressure vessel.
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    Fatigue & fracture of engineering materials & structures 20 (1997), S. 0 
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    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract— Cold-expansion of fastener holes is now commonly used within the aerospace industry to increase the fatigue endurance of airframes. Although a number of methods of cold expansion are possible, the split-sleeve cold-expansion process is the most widely accepted and is frequently used in the repair and manufacture stages of both military and civil aircraft. In the present work, the redistribution of residual hoop stresses due to the application of constant amplitude fatigue loading at 4% cold-expanded holes has been studied. A modified Sachs method was adopted to evaluate the residual stress profiles and a replication technique was used to quantify crack growth. It was found that the decay of the residual hoop stress profile near the bore of the hole was due to the initiation and growth of small fatigue cracks. Cracks were found to initiate both near and below the fatigue limit, but subsequently arrested so stabilising the overall residual stress profile.
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    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract— The factors affecting the fatigue strength of nitrided titanium were clarified. The fatigue strength depended strongly on the fracture strength of the compound layer formed on the surface by nitriding. We found a Hall-Petch relationship between the fatigue strength of nitrided titanium and the grain size. The findings indicated that the reduction in the fatigue strength by nitriding results from both the formation of the compound layer possessing low fracture strength and grain growth occurring from ordinary nitriding. Furthermore, low-temperature nitriding (620°C, 24 h) was proposed to suppress grain growth. This treatment method improved not only the wear resistance and the corrosion resistance but also the fatigue strength of titanium.
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    Teaching statistics 21 (1999), S. 0 
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    Topics: Mathematics
    Notes: This is the third and last in the short series of articles outlining the work of the organisations that sponsor Teaching Statistics.
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    Notes: A simple relationship is described which connects Buffon's classical needle problem with related problems involving circles, squares and rectangles.
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    Notes: This article reports some results of an informal study of very young children's reactions to some visual displays of data.
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    Notes: Confidence intervals are often misinterpreted. This article describes an activity which helps students understand what it means to have confidence in a Process.
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    Notes: The ability to undertake approximate calcutations and to get a “rough feel” for data is an important skill which must not be overlooked.
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    Notes: This article presents a variant on the will-known Birthday Problem.
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    Notes: Students often find the concepts of bias and consistency hard to understand intuitively. This article presnts means of demonstrating these concepts using a computer so that students, once they have seen them in action, can more readily grasp their meanings and imlications.
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    Notes: This article displays some very counter-intuitive problems of “averages” an shows one area of statistics in which vector methods play a natural role.
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    Notes: This is the second of a short series of articles briefly describing the organisations that sponsor Teaching Statistics.
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    Notes: A sampling problem is described which was given to the general public to illustrate the problems of bias and the need for randomisation when sampling.
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    Notes: Issues of measurement are fundamental in statistics but often overlooked in introductory courses. This interactive exercise encourages students to think critically about how things are measured.
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    Notes: This article explores some ideas for the imaginative use of a graphics calculator in introductory statistics teaching.
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    Notes: A sketch of the development of statistics in Australia is followed by a brief biography of one of the most important pioneers, Pat Moran.
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    Notes: Criteria for line of best fit have accessible motivations.
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    Notes: We present a simple problem that can help highlight the decision-theoretic properties of various centrality measures. We also illustrate how the ‘centrality’parameters of the classical distributions in statistics would have to be modified if we were constrained to fewer defining principles.
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    Notes: This article describes and analyses the membership and uses of the Teaching-Statistics Mailbase list, based upon a review of all messages since its inception and a recent questionnaire sent to all list members.
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    Notes: Data from the World Cup provide excellent illustrations of Poisson and exponential distributions.
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    Notes: A problem in mining engineering concerning detonators for rock blasting is considered. Simple probability calculations give very useful information about the detonation sequence.
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    Notes: Visiting industry to see how statistical methods are used in practice is well worth the time and effort which are involved.
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    Notes: A classroom practical activity for sorting lists of numbers is described, leading to some statistical analysis.
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    Notes: This is the first of a short series of articles briefly describing the organisations that sponsor Teaching Statistics. The series starts with The Royal Statistical Society.
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    Notes: This article describes the learning experiences of young children meeting stem-and-leaf plots for the first time.
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    Notes: Several measures of “success” for a simple game are discussed. Comparisons between players, and between a player and a simulation, can be made in several ways.
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    Notes: This article shows how simulation can be used to teach sampling distributions to entry level statistics students.
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    Notes: This article describes the use of Microsoft Excel, graphics calculators and a multimedia CBL package by students on an introductory statistics course.
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    Notes: A game of chance in which players can maximise their expected gain by making appropriate decisions is described. Developing an optimal strategy involves computing probabilities and conditional expected values.
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