A Stochastic Representation for Nonlocal Parabolic PDEs with Applications

Min Dai (), Steven Kou () and Chen Yang ()
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Min Dai: Department of Applied Mathematics, The Hong Kong Polytechnic University, Hong Kong SAR, China
Steven Kou: Department of Finance, Questrom School of Business, Boston University, Boston, Massachusetts 02215
Chen Yang: Department of Systems Engineering and Engineering Management, The Chinese University of Hong Kong, Hong Kong SAR, China

Mathematics of Operations Research, 2022, vol. 47, issue 3, 1707-1730

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.

Keywords: Primary: 35C99; 60H30; dual-purpose funds; Feynman–Kac representation; linear thermoelasticity; nonlocal problems; parabolic PDEs (search for similar items in EconPapers)
Date: 2022
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Persistent link: https://EconPapers.repec.org/RePEc:inm:ormoor:v:47:y:2022:i:3:p:1707-1730

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