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

TL;DR

This paper characterizes solutions to a regime-switching diffusion problem using integral equations, ensuring uniqueness and illustrating applications in option pricing models with regime changes.

Contribution

It introduces an integral equation framework for the Feynman-Kac formula in regime-switching diffusions, with conditions for solution uniqueness.

Findings

Established an integral equation characterization for regime-switching diffusions.

Provided sufficient conditions for the uniqueness of solutions.

Applied the framework to option pricing under Ornstein-Uhlenbeck regime-switching models.

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.