Infinite-Dimensional Black-Scholes Equation with Hereditary Structure |
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Authors: | Mou-Hsiung Chang Roger K. Youree |
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Affiliation: | (1) U.S. Army Research Office, P.O. Box 12211, Research Triangle Park, NC 27709, USA;(2) Instrumental Sciences Inc., P.O. Box 4711, Huntsville, AL 35811, USA |
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Abstract: | This paper considers the option pricing problem for contingent claims of the European type in a (B,S)-market in which the stock price and the asset in the riskless bank account both have hereditary structures. The Black-Scholes equation for the classical option pricing problem is generalized to an infinite-dimensional equation to include the effects of time delay in the evolution of the financial market as well as a very general payoff function. A computational algorithm for the solution is also obtained via a double sequence of polynomials of a certain bounded linear functional on a Banach space and the time variable. |
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Keywords: | Option pricing European option Generalized Black-Scholes formula Stochastic functional differential equations |
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