Spectral Approximation of Infinite-Dimensional Black-Scholes Equations with Memory

[摘要] This paper considers the pricing of a Europeanoption using a(B,S)-market in which the stock price and the asset in the riskless bank account both have hereditary price structures described by the authors of this paper (1999). Under the smoothness assumption of the payoff function, it is shown that the infinite dimensional Black-Scholes equation possesses a unique classical solution. A spectral approximation scheme is developed using the Fourier series expansion in the spaceC[−h,0]for the Black-Scholes equation. It is also shown that thenth approximant resembles the classical Black-Scholes equation in finitedimensions.

[学科分类] 应用数学