A Stochastic Representation for Nonlocal Parabolic PDEs with Applications

Abstract

We establish a stochastic representation for a class of nonlocal parabolic terminal-boundary value problems, whose terminal and boundary conditions depend on the solution in the interior domain; in particular, the solution is represented as the expectation of functionals of a diffusion process with random jumps from boundaries. We discuss three applications of the representation, the first one on the pricing of dual-purpose funds, the second one on the connection to regenerative processes, and the third one on modeling the entropy on a one-dimensional non-rigid body.

Keywords: Dual-purpose Funds, Feynman-Kac Representation, Linear Thermoelasticity, Nonlocal Problems, Parabolic PDEs