An approximation scheme for Black-Scholes equations with delays

This paper addresses a finite difference approximation for an infinite dimensional Black-Scholes equation obtained in Chang and Youree [5]. The equation arises from a consideration of an European option pricing problem in a market in which stock prices and the riskless asset prices have hereditary structures. Under a general condition on the payoff function of the option, it is shown that the pricing function is the unique viscosity solution of the infinite dimensional Black-Scholes equation. In addition, a finite difference approximation of the viscosity solution is provided and the convergence results are proved.