Option Pricing and the Dirichlet Problem
5 Pages Posted: 20 Jun 2006
Date Written: February 2006
It is well-known that the Dirichlet problem for the Laplacian on a reasonably smooth compact domain in Rn can be solved using Brownian motion. Indeed the result was found by Kakutani in 1944. In this note, I want to discuss how this result can be reinterpreted financially. Our objective is to increase our intuition about the problem rather than to attempt to prove new results.
Keywords: option pricing, Dirichlet problem, maximum principle
JEL Classification: C19
Suggested Citation: Suggested Citation