Showing a limited preview of this publication:
Abstract
Finite difference approximations to multi-asset American put option price are considered. The assets are modelled as a multi-dimensional diffusion process with variable drift and volatility. Approximation error of order one quarter with respect to the time discretisation parameter and one half with respect to the space discretisation parameter is proved by reformulating the corresponding optimal stopping problem as a solution of a degenerate Hamilton-Jacobi-Bellman equation. Furthermore, the error arising from restricting the discrete problem to a finite grid by reducing the original problem to a bounded domain is estimated.
Keywords: American put option; finite difference method; optimal stopping; optimal control; Hamilton-Jacobi-Bellman equation
Received: 2011-05-16
Revised: 2011-08-23
Accepted: 2011-09-15
Published Online: 2012
Published in Print: 2012
© Institute of Mathematics, NAS of Belarus
