A Stochastic Representation for Nonlocal Parabolic PDEs with Applications

Min Dai, Steven Kou, Chen Yang

Research output: Journal article publicationJournal articleAcademic researchpeer-review

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 nonrigid body.

Original languageEnglish
Pages (from-to)1707-1730
Number of pages24
JournalMathematics of Operations Research
Volume47
Issue number3
Early online date3 Feb 2022
DOIs
Publication statusPublished - Aug 2022

Keywords

  • Feynman–Kac representation
  • dual-purpose funds
  • linear thermoelasticity
  • nonlocal problems
  • parabolic PDEs

ASJC Scopus subject areas

  • General Mathematics
  • Computer Science Applications
  • Management Science and Operations Research

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