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  • Articles  (14,668)
  • Other Sources
  • 2000-2004  (14,668)
  • 1985-1989
  • 2004  (14,668)
  • Mathematics  (12,868)
  • Technology  (2,377)
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  • Books  (12)
  • Articles  (14,668)
  • Other Sources
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  • 2000-2004  (14,668)
  • 1985-1989
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  • 1
    Electronic Resource
    Electronic Resource
    VASIČEK BEYOND THE NORMAL (2004)
    350 Main Street , Malden , MA 02148 , USA , and 9600 Garsington Road , Oxford OX4 2DQ , UK . : Blackwell Publishers, Inc.
    Mathematical finance 14 (2004), S. 0 
    Details
    ISSN: 1467-9965
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics , Economics
    Notes: A general Ornstein-Uhlenbeck (OU) process is obtained upon replacing the Brownian motion appearing in the defining stochastic differential equation with a general Lévy process. Certain properties of the Brownian ancestor are distribution-free and carry over to the general OU process. Explicit expressions are obtainable for expected values of a number of functionals of interest also in the general case. Special attention is paid here to gamma- and Poisson-driven OU processes. The Brownian, Poisson, and gamma versions of the OU process are compared in various respects; in particular, their aptitude to describe stochastic interest rates is discussed in view of some standard issues in financial and actuarial mathematics: prices of zero-coupon bonds, moments of present values, and probability distributions of present values of perpetuities. The problem of possible negative interest rates finds its resolution in the general setup by taking the driving Lévy process to be nondecreasing.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1111/j.0960-1627.2004.00206.x
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  • 2
    Electronic Resource
    Electronic Resource
    ON THE STABILITY OF CONTINUOUS-TIME PORTFOLIO PROBLEMS WITH STOCHASTIC OPPORTUNITY SET (2004)
    350 Main Street , Malden , MA 02148 , USA , and 9600 Garsington Road , Oxford OX4 2DQ , UK . : Blackwell Publishers, Inc.
    Mathematical finance 14 (2004), S. 0 
    Details
    ISSN: 1467-9965
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics , Economics
    Notes: In this paper we present some counterexamples to show that an uncritical application of the usual methods of continuous-time portfolio optimization can be misleading in the case of a stochastic opportunity set. Cases covered are problems with stochastic interest rates, stochastic volatility, and stochastic market price of risk. To classify the problems occurring with stochastic market coefficients, we further introduce two notions of stability of portfolio problems.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1111/j.0960-1627.2004.00197.x
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  • 3
    Electronic Resource
    Electronic Resource
    QUANTO LOOKBACK OPTIONS (2004)
    350 Main Street , Malden , MA 02148 , USA , and 9600 Garsington Road , Oxford OX4 2DQ , UK . : Blackwell Publishers, Inc.
    Mathematical finance 14 (2004), S. 0 
    Details
    ISSN: 1467-9965
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics , Economics
    Notes: The lookback feature in a quanto option refers to the payoff structure where the terminal payoff of the quanto option depends on the realized extreme value of either the stock price or the exchange rate. In this paper, we study the pricing models of European and American lookback options with the quanto feature. The analytic price formulas for two types of European-style quanto lookback options are derived. The success of the analytic tractability of these quanto lookback options depends on the availability of a succinct analytic representation of the joint density function of the extreme value and terminal value of the stock price and exchange rate. We also analyze the early exercise policies and pricing behaviors of the quanto lookback options with the American feature. The early exercise boundaries of these American quanto lookback options exhibit properties that are distinctive from other two-state American option models.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1111/j.0960-1627.2004.00199.x
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  • 4
    Electronic Resource
    Electronic Resource
    Pareto Equilibria with coherent measures of risk (2004)
    350 Main Street , Malden , MA 02148 , USA , and 9600 Garsington Road , Oxford OX4 2DQ , UK . : Blackwell Publishers, Inc.
    Mathematical finance 14 (2004), S. 0 
    Details
    ISSN: 1467-9965
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics , Economics
    Notes: In this paper, we provide a definition of Pareto equilibrium in terms of risk measures, and present necessary and sufficient conditions for equilibrium in a market with finitely many traders (whom we call “banks”) who trade with each other in a financial market. Each bank has a preference relation on random payoffs which is monotonic, complete, transitive, convex, and continuous; we show that this, together with the current position of the bank, leads to a family of valuation measures for the bank. We show that a market is in Pareto equilibrium if and only if there exists a (possibly signed) measure that, for each bank, agrees with a positive convex combination of all valuation measures used by that bank on securities traded by that bank.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1111/j.0960-1627.2004.00187.x
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  • 5
    Electronic Resource
    Electronic Resource
    Hedging and Portfolio Optimization in Financial Markets with a Large Trader (2004)
    350 Main Street , Malden , MA 02148 , USA , and 9600 Garsington Road , Oxford OX4 2DQ , UK . : Blackwell Publishers, Inc.
    Mathematical finance 14 (2004), S. 0 
    Details
    ISSN: 1467-9965
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics , Economics
    Notes: We introduce a general continuous-time model for an illiquid financial market where the trades of a single large investor can move market prices. The model is specified in terms of parameter-dependent semimartingales, and its mathematical analysis relies on the nonlinear integration theory of such semimartingale families. The Itô–Wentzell formula is used to prove absence of arbitrage for the large investor, and, using approximation results for stochastic integrals, we characterize the set of approximately attainable claims. We furthermore show how to compute superreplication prices and discuss the large investor's utility maximization problem.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1111/j.0960-1627.2004.00179.x
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  • 6
    Electronic Resource
    Electronic Resource
    Approximation of Optimal Reinsurance and Dividend Payout Policies (2004)
    350 Main Street , Malden , MA 02148 , USA , and 9600 Garsington Road , Oxford OX4 2DQ , UK . : Blackwell Publishers, Inc.
    Mathematical finance 14 (2004), S. 0 
    Details
    ISSN: 1467-9965
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics , Economics
    Notes: We consider the stochastic process of the liquid assets of an insurance company assuming that the management can control this process in two ways: first, the risk exposure can be reduced by affecting reinsurance, but this decreases the premium income; and second, a dividend has to be paid out to the shareholders. The aim is to maximize the expected discounted dividend payout until the time of bankruptcy. The classical approach is to model the liquid assets or risk reserve process of the company as a piecewise deterministic Markov process. However, within this setting the control problem is very hard. Recently several papers have modeled this problem as a controlled diffusion, presuming that the policy obtained is in some sense good for the piecewise deterministic problem as well. We will clarify this statement in our paper. More precisely, we will first show that the value function of the controlled diffusion provides an asymptotic upper bound for the value functions of the piecewise deterministic problems under diffusion scaling. Finally it will be shown that the upper bound is achieved in the limit under the optimal feedback control of the diffusion problem. This property is called asymptotic optimality.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1111/j.0960-1627.2004.00183.x
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  • 7
    Electronic Resource
    Electronic Resource
    QUADRATIC TERM STRUCTURE MODELS FOR RISK-FREE AND DEFAULTABLE RATES (2004)
    350 Main Street , Malden , MA 02148 , USA , and 9600 Garsington Road , Oxford OX4 2DQ , UK . : Blackwell Publishers, Inc.
    Mathematical finance 14 (2004), S. 0 
    Details
    ISSN: 1467-9965
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics , Economics
    Notes: In this paper, quadratic term structure models (QTSMs) are analyzed and characterized in a general Markovian setting. The primary motivation for this work is to find a useful extension of the traditional QTSM, which is based on an Ornstein–Uhlenbeck (OU) state process, while maintaining the analytical tractability of the model. To accomplish this, the class of quadratic processes, consisting of those Markov state processes that yield QTSM, is introduced. The main result states that OU processes are the only conservative quadratic processes. In general, however, a quadratic potential can be added to allow QTSMs to model default risk. It is further shown that the exponent functions that are inherent in the definition of the quadratic property can be determined by a system of Riccati equations with a unique admissible parameter set. The implications of these results for modeling the term structure of risk-free and defaultable rates are discussed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1111/j.0960-1627.2004.00203.x
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  • 8
    Electronic Resource
    Electronic Resource
    A FAMILY OF TERM-STRUCTURE MODELS FOR LONG-TERM RISK MANAGEMENT AND DERIVATIVE PRICING (2004)
    350 Main Street , Malden , MA 02148 , USA , and 9600 Garsington Road , Oxford OX4 2DQ , UK . : Blackwell Publishers, Inc.
    Mathematical finance 14 (2004), S. 0 
    Details
    ISSN: 1467-9965
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics , Economics
    Notes: In this paper we propose a new family of term-structure models based on the Flesaker and Hughston (1996) positive-interest framework. The models are Markov and time homogeneous, with correlated Ornstein-Uhlenbeck processes as state variables. We provide a theoretical analysis of the one-factor model and a thorough emprical analysis of the two-factor model. This allows us to identify the key factors in the model affecting interest-rate dynamics. We conclude that the new family of models should provide a useful tool for use in long-term risk management. Suitably parameterized, they can satisfy a wide range of desirable criteria, including:〈list xml:id="l1" style="custom"〉• sustained periods of both high and low interest rates similar to the cycle lengths we have observed over the course of the 20th century in the United Kingdom and the United States• realistic probabilities of both high and low interest rates consistent with historical data and without the need for regular recalibration• a wide range of shapes of yield curves, again consistent with what we have observed in the past and including the recent Japanese yield curve.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1111/j.0960-1627.2004.00198.x
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  • 9
    Electronic Resource
    Electronic Resource
    A GENERAL FRAMEWORK FOR PRICING CREDIT RISK (2004)
    350 Main Street , Malden , MA 02148 , USA , and 9600 Garsington Road , Oxford OX4 2DQ , UK . : Blackwell Publishers, Inc.
    Mathematical finance 14 (2004), S. 0 
    Details
    ISSN: 1467-9965
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics , Economics
    Notes: A framework is provided for pricing derivatives on defaultable bonds and other credit-risky contingent claims. The framework is in the spirit of reduced-form models, but extends these models to include the case that default can occur only at specific times, such as coupon payment dates. Although the framework does not provide an efficient setting for obtaining results about structural models, it is sufficiently general to include most structural models, and thereby highlights the commonality between reduced-form and structural models. Within the general framework, multiple recovery conventions for contingent claims are considered: recovery of a fraction of par, recovery of a fraction of a no-default version of the same claim, and recovery of a fraction of the pre-default value of the claim. A stochastic-integral representation for credit-risky contingent claims is provided, and the integrand for the credit exposure part of this representation is identified. In the case of intensity-based, reduced-form models, credit spread and credit-risky term structure are studied.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1111/j.0960-1627.2004.t01-1-00193.x
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  • 10
    Electronic Resource
    Electronic Resource
    On The Fundamental Theorem Of Asset Pricing: Random Constraints And Bang-Bang No-Arbitrage Criteria (2004)
    350 Main Street , Malden , MA 02148 , USA , and 9600 Garsington Road , Oxford OX4 2DQ , UK . : Blackwell Publishers, Inc.
    Mathematical finance 14 (2004), S. 0 
    Details
    ISSN: 1467-9965
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics , Economics
    Notes: The paper generalizes and refines the Fundamental Theorem of Asset Pricing of Dalang, Morton, and Willinger (1990) in the following two respects: (a) the result is extended to a model with general portfolio constraints, and (b) versions of the no-arbitrage criterion based on the bang-bang principle in control theory are developed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1111/j.0960-1627.2004.00189.x
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