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Applied Mathematics and Optimization

, Volume 56, Issue 3, pp 395–424 | Cite as

Infinite-Dimensional Black-Scholes Equation with Hereditary Structure

  • Mou-Hsiung Chang
  • Roger K. Youree
Article

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.

Keywords

Option pricing European option Generalized Black-Scholes formula Stochastic functional differential equations 

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Copyright information

© Springer Science+Business Media, LLC 2007

Authors and Affiliations

  1. 1.U.S. Army Research OfficeResearch Triangle ParkUSA
  2. 2.Instrumental Sciences Inc.HuntsvilleUSA

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