Option Pricing and the Dirichlet Problem

Mark S. Joshi

Abstract
Laplace’s equation is ubiquitous in physics: it arises in the study of many areas such as electromagnetism, gravity and fluid dynamics since it can be used to describe the behaviour of electric, gravitational and fluid potentials. If we take a body with prescribed temperature on the boundary, then the long-term equilibrium temperature in the interior also satisfies Laplace’s equation with Dirichlet boundary conditions, that is the value of the solution on the edge is the prescribed temperature. full text