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  • Articles  (527)
  • Articles: DFG German National Licenses  (527)
  • Blackwell Publishing Ltd  (527)
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  • Mathematics  (527)
  • 1
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    Oxford, UK : Blackwell Publishing Ltd
    Mathematical finance 4 (1994), S. 0 
    ISSN: 1467-9965
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics , Economics
    Notes: The unified beta theory of Connor (1984) requires that the market portfolio be well diversified in a given factor structure. Wei (1988) extended Connor's results without relying on this assumption. This note provides an alternative to Wei's result by assuming that residuals from the projection of asset return on a set of k factors follow a joint elliptical distribution.
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  • 2
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    Oxford, UK : Blackwell Publishing Ltd
    Teaching statistics 12 (1990), S. 0 
    ISSN: 1467-9639
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics
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  • 3
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    Oxford, UK : Blackwell Publishing Ltd
    Teaching statistics 12 (1990), S. 0 
    ISSN: 1467-9639
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics
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  • 4
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    Oxford, UK : Blackwell Publishing Ltd
    Teaching statistics 12 (1990), S. 0 
    ISSN: 1467-9639
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics
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  • 5
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    Oxford, UK : Blackwell Publishing Ltd
    Teaching statistics 12 (1990), S. 0 
    ISSN: 1467-9639
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics
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  • 6
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    Oxford, UK : Blackwell Publishing Ltd
    Teaching statistics 12 (1990), S. 0 
    ISSN: 1467-9639
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics
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  • 7
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    Oxford, UK : Blackwell Publishing Ltd
    Teaching statistics 12 (1990), S. 0 
    ISSN: 1467-9639
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics
    Notes: This article reviews use of a games based resource pack with a view to its value as an aid to developing an appreciation of chance and statistics, as well as other mathematical skills, in an experiential context.
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  • 8
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    Oxford, UK : Blackwell Publishing Ltd
    Teaching statistics 12 (1990), S. 0 
    ISSN: 1467-9639
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics
    Notes: This article concerns the Kolmogorov-Smirnov one sample test which was introduced by the Russian mathematician A. N. Kolmogorov in 1933.
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  • 9
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    Oxford, UK : Blackwell Publishing Ltd
    Teaching statistics 12 (1990), S. 0 
    ISSN: 1467-9639
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics
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  • 10
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    Oxford, UK : Blackwell Publishing Ltd
    Teaching statistics 12 (1990), S. 0 
    ISSN: 1467-9639
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics
    Notes: This article provides a report on how a commonly availbale chemical database and the graphical utilities of a database management system were used to generate discussion when introducing the topics of correlation and regression to sixth form pupils.
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  • 11
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    Oxford, UK : Blackwell Publishing Ltd
    Teaching statistics 12 (1990), S. 0 
    ISSN: 1467-9639
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics
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  • 12
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    Oxford, UK : Blackwell Publishing Ltd
    Teaching statistics 11 (1989), S. 0 
    ISSN: 1467-9639
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics
    Notes: This article reports on a novel approach to teaching ideas of sampling to college students studying Urban Regional Planning.
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  • 13
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    Oxford, UK : Blackwell Publishing Ltd
    Mathematical finance 3 (1993), S. 0 
    ISSN: 1467-9965
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics , Economics
    Notes: We derive a computable approximation for the value of a European call option when prices satisfy a jump-diffusion model with the coefficients depending explicitly on time. This is achieved by approximating the original coefficients with functions that are piecewise constant in time. We give an interpretation of the approximating option values, in particular in the context of a discrete-time model associated with the approximating continuous-time model.
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  • 14
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    Oxford, UK : Blackwell Publishing Ltd
    Mathematical finance 3 (1993), S. 0 
    ISSN: 1467-9965
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics , Economics
    Notes: For a compound Poisson process with negative drift and jump distribution consisting of a mixture of exponentials on [0) and on (-, 0), an exact expression is derived for the probability of hitting the level c, c 〉 0. the problem is motivated by modeling the returns from trading on financial markets.
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  • 15
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    Oxford, UK : Blackwell Publishing Ltd
    Mathematical finance 2 (1992), S. 0 
    ISSN: 1467-9965
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics , Economics
    Notes: This paper studies contingent claim valuation of risky assets in a stochastic interest rate economy. the model employed generalizes the approach utilized by Heath, Jarrow, and Morton (1992) by imbedding their stochastic interest rate economy into one containing an arbitrary number of additional risky assets. We derive closed form formulae for certain types of European options in this context, notably call and put options on risky assets, forward contracts, and futures contracts. We also value American contingent claims whose payoffs are permitted to be general functions of both the term structure and asset prices generalizing Bensoussan (1984) and Karatzas (1988) in this regard. Here, we provide an example where an American call's value is well defined, yet there does not exist an optimal trading strategy which attains this value. Furthermore, this example is not pathological as it is a generalization of Roll's (1977) formula for a call option on a stock that pays discrete dividends.
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  • 16
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    Oxford, UK : Blackwell Publishing Ltd
    Mathematical finance 2 (1992), S. 0 
    ISSN: 1467-9965
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics , Economics
    Notes: This paper generalizes the Merton jump-diffusion option pricing model to the case in which jump risk cannot be eliminated in the market portfolio. the option pricing formula is obtained using a general equilibrium asset pricing model. Since jump risk is systematic, the correlation of the underlying stock's jump with the market portfolio's jump affects the option price.
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  • 17
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    Oxford, UK : Blackwell Publishing Ltd
    Mathematical finance 2 (1992), S. 0 
    ISSN: 1467-9965
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics , Economics
    Notes: This article develops a model for pricing the quality option embedded in the Treasury bond futures contract. Since the option value is set relative to a large family of deliverable bond prices, it is important for the theoretical bond prices to match up to the observed prices. Hence an arbitrage-based model is used where the forward rate process is initialized at its current observable value. A model for valuing the quality option in an otherwise identical forward contract is also established. This permits the quality option and marking to market costs to be separately quantified. Support is provided for the common practice of pricing Treasury bond futures contracts as forward contracts with an embedded forward quality option.
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  • 18
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    Oxford, UK : Blackwell Publishing Ltd
    Mathematical finance 2 (1992), S. 0 
    ISSN: 1467-9965
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics , Economics
    Notes: In the modern theory of finance, the valuation of derivative assets is commonly based on a replication argument. When there are transaction costs, this argument is no longer valid. In this paper, we try to address the general problem of finding the optimal portfolio among those which dominate a given derivative asset at maturity. We derive an interval for its price. the upper bound is the minimum amount one has to invest initially in order to obtain proceeds at least as valuable as the derivative asset. the lower bound is the maximum amount one can borrow initially against the proceeds of the derivative asset. We show that, in some instances, this interval may be strictly bounded above by the price of the replicating strategy. Prima facie, the cost of a dominating strategy should appear to be higher than that of the replicating one. But because trading is costly, it may pay to weigh the benefits of replication against those of potential savings on transaction costs.
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  • 19
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    Oxford, UK : Blackwell Publishing Ltd
    Mathematical finance 2 (1992), S. 0 
    ISSN: 1467-9965
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics , Economics
    Notes: We derive alternative representations of the McKean equation for the value of the American put option. Our main result decomposes the value of an American put option into the corresponding European put price and the early exercise premium. We then represent the European put price in a new manner. This representation allows us to alternatively decompose the price of an American put option into its intrinsic value and time value, and to demonstrate the equivalence of our results to the McKean equation.
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  • 20
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    Oxford, UK : Blackwell Publishing Ltd
    Mathematical finance 2 (1992), S. 0 
    ISSN: 1467-9965
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics , Economics
    Notes: probability with martingales, by david williams
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  • 21
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    Mathematical finance 2 (1992), S. 0 
    ISSN: 1467-9965
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics , Economics
    Notes: This paper explores the interest rate sensitivity of the prices of bonds and other securities when the instantaneous interest rate follows a Markov process. We show that whenever the interest rate describes a diffusion process the sensitivity of zero-coupon bonds increases with maturity. More generally, we characterize the risk-maturity relationship for contingent claims. This investigation yields a new property of option prices in the case where the underlying security price is a diffusion.
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  • 22
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    Mathematical finance 1 (1991), S. 0 
    ISSN: 1467-9965
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics , Economics
    Notes: European call options are priced when the uncertainty driving the stock price follows the V. G. stochastic process (Madan and Seneta 1990). the incomplete markets equilibrium change of measure is approximated and identified using the log return mean, variance, and kurtosis. an exact equilibrium interpretation is also provided, allowing inference about relative risk aversion coefficients from option prices. Relative to Black-Scholes, V. G. option values are higher, particularly so for out of the money options with long maturity on stocks with high means, low variances, and high kurtosis.
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  • 23
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    Mathematical finance 1 (1991), S. 0 
    ISSN: 1467-9965
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics , Economics
    Notes: This paper deals with the problem of the financial valuation of a firm and its shares of stock with general financing policies in a partial equilibrium framework. the model assumes a time-dependent discount rate and a general stochastic environment in a discrete-time setting. the fundamental valuation approach under the assumption of risk neutrality is used to obtain the time path of share price, the number of outstanding shares, and the value of the firm. These are shown to be the unique conditional expectations of certain stochastic processes. A broad class of firms for which the solution formula yields finite-valued solutions is characterized. the results are extended to the non-risk-neutral case. A regularity condition, which is both necessary and sufficient for the share price to equal the capitalization of future dividends accruing to the share, is obtained. As a mathematical aside, it is shown in the appendix that in the absence of this condition, the so-called stream of dividends approach is meaningless in the sense that it does not yield any financial valuation.
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  • 24
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    Mathematical finance 1 (1991), S. 0 
    ISSN: 1467-9965
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    Topics: Mathematics , Economics
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  • 25
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    Mathematical finance 1 (1991), S. 0 
    ISSN: 1467-9965
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    Topics: Mathematics , Economics
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  • 26
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    Mathematical finance 4 (1994), S. 0 
    ISSN: 1467-9965
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics , Economics
    Notes: We answer this question in the very general context of the n-factor Heath, Jarrow, and Morton model for the evolution of the term structure of interest rates, with nonrandom volatility. the answer is that a constraint is imposed on the behavior of the volatility structure. We explain the importance of this result for the design of efficient numerical algorithms for the valuation of options on the term structure.
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  • 27
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    Mathematical finance 4 (1994), S. 0 
    ISSN: 1467-9965
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics , Economics
    Notes: This paper extends He and Pearson's (1991) martingale approach to the study of optimal intertemporal consumption and portfolio policies with incomplete markets and short-sale constraints to a framework in which no assumptions are made on the price process for the securities. We show how both their characterization of the budget-feasible set and duality result can be extended to account for an unbounded set II of Arrow-Debreu state prices compatible with the arbitrage-free assumption. We also supply a (fairly general) sufficient condition for II to be bounded, as required in their setting.
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  • 28
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    Mathematical finance 3 (1993), S. 0 
    ISSN: 1467-9965
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics , Economics
    Notes: In this paper we use the Cox, Ingersoll, and Ross (1985b) single-factor, term structure model and extend it to the pricing of American default-free bond puts. We provide a quasi-analytical formula for these option prices based on recently established mathematical results for Bessel bridges, coupled with the optimal stopping time method. We extend our results to another interest rate contingent claim and provide a quasi-analytical solution for American yield option prices which illustrates the flexibility of our framework.
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  • 29
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    Mathematical finance 3 (1993), S. 0 
    ISSN: 1467-9965
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics , Economics
    Notes: The exponential of a scalar diffusion is considered. Point estimates of the diffusion coefficient can be obtained by considering proportional increments of different powers of the exponential. an investigation of the minimum variance estimator gives unique optimal power.
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    Mathematical finance 3 (1993), S. 0 
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    Topics: Mathematics , Economics
    Notes: Several risk-neutral expectation formulae are derived in a general multifactor setting. Specializing to deterministic covariances of returns, they lead to formulae for forward and future prices as well as formulae for options on forward and futures contracts. the results are applicable to currencies, bonds, commodities with stochastic convenience yield, and stock indices. For currencies, a noarbitrage relation between domestic and foreign economies is formulated and applied to evaluate quanto futures and options.
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  • 31
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    Mathematical finance 3 (1993), S. 0 
    ISSN: 1467-9965
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics , Economics
    Notes: The aim of this paper is to develop a model for the pricing of European options under the assumption of a stochastic interest rate in a discrete-time context. This is accomplished by combining the well-known binomial model for a stock with a binomial model for the spot interest rate.
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  • 32
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    Mathematical finance 3 (1993), S. 0 
    ISSN: 1467-9965
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics , Economics
    Notes: An empirical version of the Cox, Ingersoll, and Ross (1985a) call option pricing model is derived, assuming execution price uncertainty in the options market. the pricing restrictions come in the form of moment conditions in the option pricing error. These can be estimated and tested using a version of the method of simulated moments (MSM). Simulation estimates, obtained by discretely approximating the risk-neutral processes of the underlying stock price and the interest rate, are substituted for analytically unknown call prices. the asymptotics and other aspects of the MSM estimator are discussed. the model is tested on transaction prices at 15-minute intervals. It substantially outperforms the Black-Scholes model. the empirical success of the Cox-Ingersoll-Ross model implies that the continuous-time interest rate implicit in synchronous transaction quotes of 90-day Treasury-bill futures contracts is an-albeit noisy-proxy for the instantaneous volatility on common stock. the process of the instantaneous volatility is found to be close to nonstationary. It is well approximated by a heteroskedastic unit-root process. With this approximation, the Cox-Ingersoll-Ross model only slightly overprices long-maturity options.
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  • 33
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    Mathematical finance 3 (1993), S. 0 
    ISSN: 1467-9965
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics , Economics
    Notes: We analyze the optimal risky investment policy for an investor who, at each point in time, wants to lose no more than a fixed percentage of the maximum value his wealth has achieved up to that time. In particular, if Mt is the maximum level of wealth W attained on or before time t, then the constraint imposed on his portfolio choice is that WtαMt, where α is an exogenous number betweenα O and 1. We show that, for constant relative risk aversion utility functions, the optimal policy involves an investment in risky assets at time t in proportion to the “surplus”Wt - αMt. the optimal policy may appear similar to the constant-proportion portfolio insurance policy analyzed in Black and Perold (1987) and Grossman and Vila (1989). However, in those papers, the investor keeps his wealth above a nonstochastic floor F instead of a stochastic floor αMt. the stochastic character of the floor studied here has interesting effects on the investment policy in states of nature when wealth is at an all-time high; i.e., when Wt =Mt. It can be shown that at Wt=Mt, αMt is expected to grow at a faster rate than Wt, and therefore the investment in the risky asset can be expected to fall. We also show that the investment in the risky asset can be expected to rise when Wt is close to αMt. We conjecture that in an equilibrium model the stochastic character of the floor creates “resistance” levels as the market approaches an all-time high (because of the reluctance of investors to take more risk when Wt=Mt).
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  • 34
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    Mathematical finance 3 (1993), S. 0 
    ISSN: 1467-9965
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    Topics: Mathematics , Economics
    Notes: This paper derives the equilibrium excess returns on risky assets in an exchange economy where the underlying exogenous uncertainty is a combination of a pure multidimensional jump process and a diffusion model. We derive closed-form solutions for the interest rate and the risk premiums on risky assets for a traditional class of separable utility indices. Our analysis demonstrates that when the underlying jumps of the aggregate consumption process are not negligible, then the traditional form of the consumption-based capital asset princing model need not hold and the asset risk premiums may be larger than predicted by the traditional CCAPM in continuous time, based on pure Itô diffusion processes. Our analysis suggests an explanation for the large estimates of the risk premiums reported in empirical tests of the single-beta CCAPM.
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    Mathematical finance 3 (1993), S. 0 
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    Topics: Mathematics , Economics
    Notes: This paper treats the problem of consumption and portfolio choice in continuous time, with stochastic income that cannot be replicated by trading the available securities. the optimal controls and value functions are characterized in terms of the viscosity solution of the associated Hamilton-Jacobi-Bellman equation, which is shown to exist and is characterized. the optimal policy is then given from the first-order conditions of the Hamilton-Jacobi-Bellman equation.
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    Mathematical finance 3 (1993), S. 0 
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    Topics: Mathematics , Economics
    Notes: We consider the American put option in the Black-Scholes model. When the value of the option is computed through numerical methods (such as the binomial method and the finite difference method) the approximation yields an approximate critical price. We prove the convergence of this approximate critical price towards the exact critical price.
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    Mathematical finance 3 (1993), S. 0 
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    Topics: Mathematics , Economics
    Notes: This paper studies the moments of some exponential-integral functionals of Bessel processes, which are of interest in some questions of mathematical finance, including the valuation of perpetuities and Asian options.
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    Mathematical finance 3 (1993), S. 0 
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    Topics: Mathematics , Economics
    Notes: This paper studies a class of diffusion models for stock prices derived by a microeconomic approach. We consider discrete-time processes resulting from a market equilibrium and then apply an invariance principle to obtain a continuous-time model. the resulting process is an Ornstein-Uhlenbeck process in a random environment, and we analyze its qualitative behavior. In particular, we provide simple criteria for the stability or instability of the corresponding stock price model, and we give explicit formulae for the invariant distributions in the recurrent case.
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    Mathematical finance 2 (1992), S. 0 
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    Topics: Mathematics , Economics
    Notes: We establish necessary and sufficient conditions for an H1-martingale to be representable with respect to a collection, of local martingales. M H1(P) is representable if and only if M is a local martingale under all p.m.'s Q which are “uniformly equivalent” to P and which make all the elements of local martingales (Theorem 1.1). We then give necessary and sufficient conditions which are easier to verify, and only involve expectations (Theorem 1.2). We go on to apply these results to the problem of pricing claims in an incomplete financial market-establishing two conjectures of Harrison and Pliska(1981).
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    Mathematical finance 2 (1992), S. 0 
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    Topics: Mathematics , Economics
    Notes: This paper provides a general valuation method for the European options whose payoff is restricted by curved boundaries contractually set on the underlying asset price process when it follows the geometric Brownian motion. Our result is based on the generalization of the Levy formula on the Brownian motion by T. W. Anderson in sequential analysis. We give the explicit probability formula that the geometric Brownian motion reaches in an interval at the maturity date without hitting either the lower or the upper curved boundaries. Although the general pricing formulae for options with boundaries are expressed as infinite series in the general case, our numerical study suggests that the convergence of the series is rapid. Our results include the formulae for options with a lower boundary by Merton (1973), for path-dependent options by Goldman, Sossin, and Gatto (1979), and for some corporate securities as special cases.
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    Mathematical finance 2 (1992), S. 0 
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    Topics: Mathematics , Economics
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    Mathematical finance 4 (1994), S. 0 
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    Topics: Mathematics , Economics
    Notes: Given a sequence of discrete-time option valuation models in which the sequence of processes defining the state variables converges weakly to a diffusion, we prove that the sequence of American option values obtained from these discrete-time models also converges to the corresponding value obtained from the continuous-time model for the standard models in the finance/economics literature. the convergence proof carries over to the case when the limiting risky asset price process follows a diffusion, except it pays discrete dividends on some fixed dates.
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    Mathematical finance 4 (1994), S. 0 
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    Topics: Mathematics , Economics
    Notes: The note deals with the pricing of American options related to foreign market equities. the form of the early exercise premium representation of the American option's price in a stochastic interest rate economy is established. Subsequently, the American fixed exchange rate foreign equity option and the American equity-linked foreign exchange option are studied in detail.
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    Mathematical finance 4 (1994), S. 0 
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    Notes: Working within the Heath-Jarrow-Morton framework and using the theory of stochastic equations in infinite dimensions, a useful multifactor Gauss-Markov model for the movement of the whole of the yield curve is derived. Swaptions are priced. They are hedged by eliminating random terms between the semimartingale representations of the swaption and hedging instruments. Hedging efficiency is analyzed. the model is fitted to the swap/cap strips in Australia. Computation times on a 20-MHz laptop computer are acceptable.
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    Notes: This paper develops a cross-market version of factor pricing models. It is shown that exact factor pricing holds across two submarkets with respect to their common factors if and only if the unique pricing operator for the first submarket is equal to that for the other submarket with probability 1. We define an APT measure as the squared distance between the two pricing operators. Then, testing whether this measure is zero is equivalent to testing exact factor pricing across the two submarkets. Since the estimation of this measure does not require parameterizing and extracting the underlying factors, one can test factor pricing models without knowing any factors. In addition, we present a randomization procedure so that one can use it to conduct a more comprehensive investigation on the empirical robustness of factor pricing models.
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    Notes: This article develops a general methodology that uses the observed prices of a derivative contract to compute maximum likelihood parameter estimates for an unobserved asset value process. the use of this estimation methodology is demonstrated in two applications: Vasicek's term structure model and deposit insurance pricing. This methodology can also be useful in the empirical analysis of complex financial contracts involving embedded options.
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    Mathematical finance 4 (1994), S. 0 
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    Notes: Threshold autoregressive (TAR) models condition the first moment of a time series on lagged information using a step-function-type nonlinear structure. TAR techniques are expected to be relevant in financial time-series modeling in situations where deviations of prices from equilibrium values depend on discrete transaction costs and where market regulators follow intervention rules based on threshold values of control variables. an important finance application is in modeling the difference in prices of equivalent assets in the presence of transaction costs. the focus of this paper is on motivating the use of TAR models in this context and on the statistical estimation and testing procedures. the procedures are illustrated by modeling the difference between the prices of an index futures contract and the equivalent underlying cash index. It is found that the hypothesis of linearity is conclusively rejected in favor of threshold nonlinearity and that the estimated thresholds are largely consistent with arbitrage-related transaction costs.
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    Notes: Let (St)tεI be an Rd-valued adapted stochastic process on (Ω, ?, (?t)tεI, P). A basic problem occurring notably in the analysis of securities markets, is to decide whether there is a probability measure Q on ? equivalent to P such that (St)tεI is a martingale with respect to Q. It is known (see the fundamental papers of Harrison and Kreps 1979; Harrison and Pliska 1981; and Kreps 1981) that there is an intimate relation of this problem with the notions of “no arbitrage” and “no free lunch” in financial economics. We introduce the intermediate concept of “no free lunch with bounded risk.” This is a somewhat more precise version of the notion of “no free lunch.” It requires an absolute bound of the maximal loss occurring in the trading strategies considered in the definition of “no free lunch.” We give an argument as to why the condition of “no free lunch with bounded risk” should be satisfied by a reasonable model of the price process (St)tεI of a securities market. We can establish the equivalence of the condition of “no free lunch with bounded risk” with the existence of an equivalent martingale measure in the case when the index set I is discrete but (possibly) infinite. A similar theorem was recently obtained by Delbaen (1992) for continuous-time processes with continuous paths. We can combine these two theorems to get a similar result for the continuous-time case when the process (St)tεR+ is bounded and, roughly speaking, the jumps occur at predictable times. In the infinite horizon setting, the price process has to be “almost a martingale” in order to allow an equivalent martingale measure.
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    Mathematical finance 3 (1993), S. 0 
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    Notes: Using Bessel processes, one can solve several open problems involving the integral of an exponential of Brownian motion. This point will be illustrated with three examples. The first one is a formula for the Laplace transform of an Asian option which is “out of the money.”The second example concerns volatility misspecification in portfolio insurance strategies, when the stochastic volatility is represented by the Hull and White model. The third one is the valuation of perpetuities or annuities under stochastic interest rates within the Cox-Ingersoll-Ross framework. Moreover, without using time changes or Bessel processes, but only simple probabilistic methods, we obtain further results about Asian options: the computation of the moments of all orders of an arithmetic average of geometric Brownian motion; the property that, in contrast with most of what has been written so far, the Asian option may be more expensive than the standard option (e.g., options on currencies or oil spreads); and a simple, closed-form expression of the Asian option price when the option is “in the money,” thereby illuminating the impact on the Asian option price of the revealed underlying asset price as time goes by. This formula has an interesting resemblance with the Black-Scholes formula, even though the comparison cannot be carried too far.
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    Notes: The price of a risky asset § is described by a Markov diffusion with jumps. In general there may be many equivalent martingale measures. Contingent claims which depend on the price of § at some time T may not be attainable, and the market may not be complete. However, using a martingale representation result, the local risk-minimizing strategy is explicitly constructed. This in turn provides a new motivation for the concept of the minimal martingale measure.
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    Notes: A consol is a default-free financial instrument paying a constant stream of one unit of money. A synonym is a perpetuity. the valuation of a consol presents a particular difficulty: the time horizon of this instrument is infinity, and hence the usual technique of replacing the physical probability measure by a new probability measure represents serious problems with regard to absolute continuity of the two measures. We will work out explicit formulas when the instantaneous riskless interest rate follows a square-root process under the risk-free measure. Several mathematical properties will be investigated. Yor and Geman and Yor have considered the problem of pricing consols and carry out a more fundamental analysis (see References). This paper is self-contained and emphasizes properties or techniques not covered by those authors.
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    Mathematical finance 2 (1992), S. 0 
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    Notes: We consider a very general diffusion model for asset prices which allows the description of stochastic and past-dependent volatilities. Since this model typically yields an incomplete market, we show that for the purpose of pricing options, a small investor should use the minimal equivalent martingale measure associated to the underlying stock price process. Then we present stochastic numerical methods permitting the explicit computation of option prices and hedging strategies, and we illustrate our approach by specific examples.
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    Notes: Conditions suitable for applications in finance are given for the weak convergence (or convergence in probability) of stochastic integrals. For example, consider a sequence Sn of security price processes converging in distribution to S and a sequence θn of trading strategies converging in distribution to θ. We survey conditions under which the financial gain process θn dSn converges in distribution to θ dS. Examples include convergence from discrete- to continuous-time settings and, in particular, generalizations of the convergence of binomial option replication models to the Black-Scholes model. Counterexamples are also provided.
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    Notes: Book review in this Article financial engineering: a handbook of derivative products, by S. eckl, J. N. robinson, and D. C. Thomas
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    Notes: We use a martingale approach to study optimal intertemporal consumption and portfolio policies in a general discrete-time, discrete-state-space securities market with dynamically incomplete markets and short-sale constraints. We characterize the set of feasible consumption bundles as the budget-feasible set defined by constraints formed using the extreme points of the closure of the set of Arrow-Debreu state prices consistent with no arbitrage, and then establish a relationship between the original problem and a dual minimization problem.
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    Notes: Let X denote a positive Markov stochastic integral, and let S(t, μ) = exp(μt)X(t) represent the price of a security at time t with infinitesimal rate of return μ. Contingent claim (option) pricing formulas typically do not depend on μ. We show that if a contingent claim is not equivalent to a call option having exercise price equal to zero, then security prices having this property—option prices do not depend on μ—must satisfy: for some V (0, T), In(S(t, μ)X(V)) is Gaussian on a time interval [V, T], and hence S(t, μ) has independent observed returns. With more assumptions, V= 0, and there exist equivalent martingale measures.
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    Notes: We show that the problem of pricing the American put is equivalent to solving an optimal stopping problem. the optimal stopping problem gives rise to a parabolic free-boundary problem. We show there is a unique solution to this problem which has a lower boundary. We identify an integral equation solved by the boundary and show that it is the unique solution to this equation satisfying certain natural additional conditions. the proofs also give a natural decomposition of the price of the American option as the sum of the price of the European option and an “American premium.”
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    Notes: We exhibit an algorithm for portfolio selection that asymptotically outperforms the best stock in the market. Let xi= (xi, xi2,…, xim)t denote the performance of the stock market on day i, where xii is the factor by which the jth stock increases on day i. Let bi= (bi1 bi2, bim)t, b;ij≫ 0, bij= 1, denote the proportion bij of wealth invested in the j th stock on day i. Then Sn= IIin= bitxi is the factor by which wealth is increased in n trading days. Consider as a goal the wealth Sn*= maxb IIin=1 btxi that can be achieved by the best constant rebalanced portfolio chosen after the stock outcomes are revealed. It can be shown that Sn * exceeds the best stock, the Dow Jones average, and the value line index at time n. In fact, Sn* usually exceeds these quantities by an exponential factor. Let x1, x2, be an arbitrary sequence of market vectors. It will be shown that the nonanticipating sequence of portfolios 〈inlineGraphic alt="inline image" href="urn:x-wiley:09601627:MAFI1:MAFI_1_mu1" location="equation/MAFI_1_mu1.gif"/〉 db yields wealth 〈inlineGraphic alt="inline image" href="urn:x-wiley:09601627:MAFI1:MAFI_1_mu2" location="equation/MAFI_1_mu2.gif"/〉 such that 〈inlineGraphic alt="inline image" href="urn:x-wiley:09601627:MAFI1:MAFI_1_mu3" location="equation/MAFI_1_mu3.gif"/〉, for every bounded sequence x1, x2…, and, under mild conditions, achieve〈displayedItem type="mathematics" xml:id="mu4" numbered="no"〉〈mediaResource alt="image" href="urn:x-wiley:09601627:MAFI1:MAFI_1_mu4"/〉where J, is an (m - 1) x (m - I) sensitivity matrix. Thus this portfolio strategy has the same exponential rate of growth as the apparently unachievable S*n.
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    Notes: In this paper, we study the risk-aversion behavior of an agent in the dynamic framework of consumption/investment decision making that allows the possibility of bankruptcy. Agent's consumption utility is assumed to be represented by a strictly increasing, strictly concave, continuously differentiable function in the general case and by a HARA-type function in the special case treated in the paper. Coefficients of absolute and relative risk aversion are defined to be the well-known curvature measures associated with the derived utility of wealth obtained as the value function of the agent's optimization problem. Through an analysis of these coefficients, we show how the change in agent's risk aversion as his wealth changes depends on his consumption utility and the other problem parameters, including the payment at bankruptcy. Moreover, in the HARA case, we can conclude that the agent's relative risk aversion is nondecreasing with wealth, while his absolute risk aversion is decreasing with wealth only if he is sufficiently wealthy. At lower wealth levels, however, the agent's absolute risk aversion may increase with wealth in some cases.
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    Notes: Book reviewed in this Article:Probability and Statistics with Reliability, Queuing and Computer Science Applications. By K. S. TrivediIntroducing Social Statistics. By R. Startup and E. T. Whittaker. George Allen and Unwin. 1982. Studies in Sociology: 12. 201 pagesSuccess in Statistics. By Fred Caswell.How to Tell the Liars from the Statisticians. By Robert Hooke. Marcel Dekker, 1983. 173 pages (hardback).
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    Notes: Book reviewed in this Article:Notes Towards a History of Teaching Statistics. By J. Bibby.Work Out Operational Research. By T. A. Burley and G. O'Sullivan.
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    Notes: The following short contributions are from people who attended the Second International Conference on Teaching Statistics held in Victoria, August 1986
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    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics
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    Teaching statistics 9 (1987), S. 0 
    ISSN: 1467-9639
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics
    Notes: Teaching with a Micro. Maths 3. Shell Centre for Mathematical Education, Nottingham. £12.00 +£1.00 post and packing. Disc with teaching booklet.
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    Topics: Mathematics
    Notes: Educated Guessing. How to cope in an uncertain world. By S. Kotz & D. F. StroupMastering Statistics with your microcomputer. By C. Boyle.Applied and Computational Statistics: A first course. By K. D. C. Stoodley.Also Received in the Macmillan Work Out Series.P. Stevens. Work Out Principles of Accounts ‘O’ Level and GCSE.G. D. Buckwell. Work Out Mathematics ‘O’ Level and GCSE.B. Haines and R. Haines. Work Out Pure Mathematics A-Level. 223 pages. £5.95.
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    Teaching statistics 8 (1986), S. 0 
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    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics
    Type of Medium: Electronic Resource
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