Option Pricing and the Dirichlet Problem

Joshi, Mark S.

doi:10.2139/ssrn.909023

Option Pricing and the Dirichlet Problem

5 Pages Posted: 20 Jun 2006

See all articles by Mark S. Joshi

Mark S. Joshi

University of Melbourne - Centre for Actuarial Studies (deceased)

Date Written: February 2006

Abstract

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

Joshi, Mark, Option Pricing and the Dirichlet Problem (February 2006). Available at SSRN: https://ssrn.com/abstract=909023 or http://dx.doi.org/10.2139/ssrn.909023