Integral equation characterization of the Feynman–Kac formula for a regime-switching diffusion

Abstract

In this paper, we provide an integral equation characterization of the solution to a Cauchy problem associated to the Feynman–Kac formula for a regime-switching diffusion. We give a sufficient condition to guarantee the uniqueness of solutions to the integral equation and provide an example in the context of option pricing under the Ornstein–Uhlenbeck regime-switching model. Keywords: Cauchy problem, Feynman–Kac, Regime-switching, Integral equation, Contraction mapping