A Stochastic Representation for Nonlocal Parabolic PDEs with Applications

• 成果类型: Article; Early Access
• 署名作者: Dai, Min; Kou, Steven; Yang, Chen
• 署名单位: Hong Kong Polytechnic University; Boston University; Chinese University of Hong Kong
• 刊物名称: MATHEMATICS OF OPERATIONS RESEARCH
• ISSN/ISSBN: 0364-765X
• DOI: 10.1287/moor.2020.1061
• 发表日期: 2022
• 关键词: reaction-diffusion equations; heat-equation; BOUNDARY; decay

摘要

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.