Spherical Harmonics Applied to Differential and Integro-Differential Equations Arising in Mathematical Finance

Abstract

This paper is devoted to extend the spherical harmonics technique to the solution of parabolic differential equations and to integro-differential equations. The heat equation and the Black–Scholes equation are solved by using the method of spherical harmonics. We also discuss the Black–Scholes equation in annular domains, and generalized Black–Scholes equations. Finally we solve some integro-differential equation arising in financial models with jumps by using the method of spherical harmonics.