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  • Articles  (183,832)
  • Articles: DFG German National Licenses  (183,832)
  • Mathematics  (183,832)
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  • Articles  (183,832)
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  • 1
    Electronic Resource
    Electronic Resource
    MINIMAL ENTROPY–HELLINGER MARTINGALE MEASURE IN INCOMPLETE MARKETS (2005)
    350 Main Street , Malden , MA 02148 , USA , and 9600 Garsington Road , Oxford OX4 2DQ , UK . : Blackwell Publishing, Inc.
    Mathematical finance 15 (2005), S. 0 
    Details
    ISSN: 1467-9965
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics , Economics
    Notes: This paper defines an optimization criterion for the set of all martingale measures for an incomplete market model when the discounted price process is bounded and quasi-left continuous. This criterion is based on the entropy–Hellinger process for a nonnegative Doléans–Dade exponential local martingale. We develop properties of this process and establish its relationship to the relative entropy “distance.” We prove that the martingale measure, minimizing this entropy–Hellinger process, is unique. Furthermore, it exists and is explicitly determined under some mild conditions of integrability and no arbitrage. Different characterizations for this extremal risk-neutral measure as well as immediate application to the exponential hedging are given. If the discounted price process is continuous, the minimal entropy–Hellinger martingale measure simply is the minimal martingale measure of Föllmer and Schweizer. Finally, the relationship between the minimal entropy–Hellinger martingale measure (MHM) and the minimal entropy martingale measure (MEM) is provided. We also give an example showing that in contrast to the MHM measure, the MEM measure is not robust with respect to stopping.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1111/j.1467-9965.2005.00229.x
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  • 2
    Electronic Resource
    Electronic Resource
    ON UTILITY-BASED PRICING OF CONTINGENT CLAIMS IN INCOMPLETE MARKETS (2005)
    350 Main Street , Malden , MA 02148 , USA , and 9600 Garsington Road , Oxford OX4 2DQ , UK . : Blackwell Publishing, Inc.
    Mathematical finance 15 (2005), S. 0 
    Details
    ISSN: 1467-9965
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics , Economics
    Notes: We study the uniqueness of the marginal utility-based price of contingent claims in a semimartingale model of an incomplete financial market. In particular, we obtain that a necessary and sufficient condition for all bounded contingent claims to admit a unique marginal utility-based price is that the solution to the dual problem defines an equivalent local martingale measure.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1111/j.0960-1627.2005.00217.x
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  • 3
    Electronic Resource
    Electronic Resource
    OPTIMAL REINSURANCE AND DIVIDEND DISTRIBUTION POLICIES IN THE CRAMÉR-LUNDBERG MODEL (2005)
    350 Main Street , Malden , MA 02148 , USA , and 9600 Garsington Road , Oxford OX4 2DQ , UK . : Blackwell Publishing, Inc.
    Mathematical finance 15 (2005), S. 0 
    Details
    ISSN: 1467-9965
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics , Economics
    Notes: We consider that the reserve of an insurance company follows a Cramér-Lundberg process. The management has the possibility of controlling the risk by means of reinsurance. Our aim is to find a dynamic choice of both the reinsurance policy and the dividend distribution strategy that maximizes the cumulative expected discounted dividend payouts. We study the usual cases of excess-of-loss and proportional reinsurance as well as the family of all possible reinsurance contracts. We characterize the optimal value function as the smallest viscosity solution of the associated Hamilton-Jacobi-Bellman equation and we prove that there exists an optimal band strategy. We also describe the optimal value function for small initial reserves.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1111/j.0960-1627.2005.00220.x
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  • 4
    Electronic Resource
    Electronic Resource
    UNIVERSAL INVESTMENT IN MARKETS WITH TRANSACTION COSTS (2005)
    350 Main Street , Malden , MA 02148 , USA , and 9600 Garsington Road , Oxford OX4 2DQ , UK . : Blackwell Publishing, Inc.
    Mathematical finance 15 (2005), S. 0 
    Details
    ISSN: 1467-9965
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics , Economics
    Notes: In this paper we investigate growth optimal investment in two-asset discrete-time markets with proportional transaction costs and no distributional assumptions on the market return sequences. We construct a policy with growth rate at least as large as any interval policy. Since interval policies are ε-optimal for independent and identically distributed (i.i.d.) markets (Iyengar 2002), it follows that our policy when employed in an i.i.d. market is able to “learn” the optimal interval policy and achieve growth optimality; in other words, it is a universal growth optimal policy for i.i.d. markets.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1111/j.0960-1627.2005.00223.x
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  • 5
    Electronic Resource
    Electronic Resource
    STOCHASTIC HYPERBOLIC DYNAMICS FOR INFINITE-DIMENSIONAL FORWARD RATES AND OPTION PRICING (2005)
    350 Main Street , Malden , MA 02148 , USA , and 9600 Garsington Road , Oxford OX4 2DQ , UK . : Blackwell Publishing, Inc.
    Mathematical finance 15 (2005), S. 0 
    Details
    ISSN: 1467-9965
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics , Economics
    Notes: We model the term-structure modeling of interest rates by considering the forward rate as the solution of a stochastic hyperbolic partial differential equation. First, we study the arbitrage-free model of the term structure and explore the completeness of the market. We then derive results for the pricing of general contingent claims. Finally we obtain an explicit formula for a forward rate cap in the Gaussian framework from the general results.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1111/j.0960-1627.2005.00209.x
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  • 6
    Electronic Resource
    Electronic Resource
    EXISTENCE OF AN EQUILIBRIUM WITH DISCONTINUOUS PRICES, ASYMMETRIC INFORMATION, AND NONTRIVIAL INITIAL σ-FIELDS (2005)
    350 Main Street , Malden , MA 02148 , USA , and 9600 Garsington Road , Oxford OX4 2DQ , UK . : Blackwell Publishing, Inc.
    Mathematical finance 15 (2005), S. 0 
    Details
    ISSN: 1467-9965
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics , Economics
    Notes: In this paper, we solve the problems of optimization and equilibrium on a continuous-time financial market with discontinuous prices, in which agents have different random endowments and different information on the structure and future behavior of the prices. Our purpose is to go over and to extend the work of Pikovsky and Karatzas (1996) by using the theory developed by Amendinger (2000) about martingale representation theorems for initially enlarged filtrations, and to generalize the results in the case of discontinuous prices.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1111/j.0960-1627.2005.00212.x
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  • 7
    Electronic Resource
    Electronic Resource
    A QUANTIZATION TREE METHOD FOR PRICING AND HEDGING MULTIDIMENSIONAL AMERICAN OPTIONS (2005)
    350 Main Street , Malden , MA 02148 , USA , and 9600 Garsington Road , Oxford OX4 2DQ , UK . : Blackwell Publishing, Inc.
    Mathematical finance 15 (2005), S. 0 
    Details
    ISSN: 1467-9965
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics , Economics
    Notes: We present here the quantization method which is well-adapted for the pricing and hedging of American options on a basket of assets. Its purpose is to compute a large number of conditional expectations by projection of the diffusion on optimal grids designed to minimize the (square mean) projection error (Graf and Luschgy 2000). An algorithm to compute such grids is described. We provide results concerning the orders of the approximation with respect to the regularity of the payoff function and the global size of the grids. Numerical tests are performed in dimensions 2, 4, 5, 6, 10 with American style exchange options. They show that theoretical orders are probably pessimistic.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1111/j.0960-1627.2005.00213.x
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  • 8
    Electronic Resource
    Electronic Resource
    A NOTE ON NONAFFINE SOLUTIONS OF TERM STRUCTURE EQUATIONS WITH APPLICATIONS TO POWER EXCHANGES (2005)
    350 Main Street , Malden , MA 02148 , USA , and 9600 Garsington Road , Oxford OX4 2DQ , UK . : Blackwell Publishing, Inc.
    Mathematical finance 15 (2005), S. 0 
    Details
    ISSN: 1467-9965
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics , Economics
    Notes: A method based on transformations of well-known solutions of term structure equations is presented in order to incorporate Martin Barlow's spot price model for electricity into a model for future prices on electricity. The setting for the evolution of term structures is chosen in the spirit of Da Prato and Zabczyk.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1111/j.0960-1627.2005.00216.x
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  • 9
    Electronic Resource
    Electronic Resource
    STOCHASTIC VOLATILITY MODELS, CORRELATION, AND THE q-OPTIMAL MEASURE (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 aim of this paper is to study the minimal entropy and variance-optimal martingale measures for stochastic volatility models. In particular, for a diffusion model where the asset price and volatility are correlated, we show that the problem of determining the q-optimal measure can be reduced to finding a solution to a representation equation. The minimal entropy measure and variance-optimal measure are seen as the special cases q= 1 and q= 2 respectively. In the case where the volatility is an autonomous diffusion we give a stochastic representation for the solution of this equation. If the correlation ρ between the traded asset and the autonomous volatility satisfies ρ2 〈 1/q, and if certain smoothness and boundedness conditions on the parameters are satisfied, then the q-optimal measure exists. If ρ2≥ 1/q, then the q-optimal measure may cease to exist beyond a certain time horizon. As an example we calculate the q-optimal measure explicitly for the Heston model.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1111/j.0960-1627.2004.00204.x
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  • 10
    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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