A Stochastic Representation for Nonlocal Parabolic PDEs with Applications
Min Dai, Steven G. Kou, Chen Yang · Mathematics of Operations Research · 2022
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 nonrigid body.