A Stochastic Representation for Nonlocal Parabolic PDEs with Applications

Mathematics of Operations Research

32 Pages Posted:

See all articles by Min Dai

Min Dai

National University of Singapore (NUS) - Department of Mathematics

Steven Kou

Boston University

Chen Yang

The Chinese University of Hong Kong (CUHK) - Department of Systems Engineering and Engineering Management

Date Written: April 12, 2019

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

Suggested Citation

Dai, Min and Kou, Steven and Yang, Chen, A Stochastic Representation for Nonlocal Parabolic PDEs with Applications (April 12, 2019). Mathematics of Operations Research. Available at SSRN: https://ssrn.com/abstract=

Min Dai

National University of Singapore (NUS) - Department of Mathematics ( email )

Singapore

Steven Kou (Contact Author)

Boston University ( email )

595 Commonwealth Avenue
Boston, MA 02215
United States
6173583318 (Phone)

Chen Yang

The Chinese University of Hong Kong (CUHK) - Department of Systems Engineering and Engineering Management ( email )

Hong Kong
China

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