A Stochastic Representation for Nonlocal Parabolic PDEs with Applications

Min Dai; Steven Kou; Chen Yang

doi:10.1287/moor.2020.1061

A Stochastic Representation for Nonlocal Parabolic PDEs with Applications

Min Dai, Steven Kou, Chen Yang

Research output: Journal article publication › Journal article › Academic research › peer-review

2 Citations (Scopus)

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 language	English
Pages (from-to)	1707-1730
Number of pages	24
Journal	Mathematics of Operations Research
Volume	47
Issue number	3
Early online date	3 Feb 2022
DOIs	https://doi.org/10.1287/moor.2020.1061
Publication status	Published - 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

More information

10.1287/moor.2020.1061

Cite this

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title = "A Stochastic Representation for Nonlocal Parabolic PDEs with Applications",

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 = "Feynman–Kac representation, dual-purpose funds, linear thermoelasticity, nonlocal problems, parabolic PDEs",

author = "Min Dai and Steven Kou and Chen Yang",

note = "Funding Information: Funding: The research of M. Dai is supported in part by the National Natural Science Foundation of China (NSFC) [Grant 11671292], and Singapore Ministry of Education (MOE) Academic Research Fund [Grants R-146-000-243-114 and R-703-000-032-112]. The research of S. Kou was supported in part by the NSFC [Grant 71571129] and Singapore MOE [Grant MOE2017-T2-1-101]. The research of C. Yang is supported in part by a Chinese University of Hong Kong (CUHK) start-up fund, and CUHK Direct Grant [Grant 4055132]. Publisher Copyright: Copyright: {\textcopyright} 2022 INFORMS.",

year = "2022",

month = aug,

doi = "10.1287/moor.2020.1061",

language = "English",

volume = "47",

pages = "1707--1730",

journal = "Mathematics of Operations Research",

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AU - Dai, Min

AU - Kou, Steven

AU - Yang, Chen

N1 - Funding Information: Funding: The research of M. Dai is supported in part by the National Natural Science Foundation of China (NSFC) [Grant 11671292], and Singapore Ministry of Education (MOE) Academic Research Fund [Grants R-146-000-243-114 and R-703-000-032-112]. The research of S. Kou was supported in part by the NSFC [Grant 71571129] and Singapore MOE [Grant MOE2017-T2-1-101]. The research of C. Yang is supported in part by a Chinese University of Hong Kong (CUHK) start-up fund, and CUHK Direct Grant [Grant 4055132]. Publisher Copyright: Copyright: © 2022 INFORMS.

PY - 2022/8

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N2 - 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.

AB - 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.

KW - Feynman–Kac representation

KW - dual-purpose funds

KW - linear thermoelasticity

KW - nonlocal problems

KW - parabolic PDEs

UR - http://www.scopus.com/inward/record.url?scp=85140012534&partnerID=8YFLogxK

U2 - 10.1287/moor.2020.1061

DO - 10.1287/moor.2020.1061

M3 - Journal article

SN - 0364-765X

VL - 47

SP - 1707

EP - 1730

JO - Mathematics of Operations Research

JF - Mathematics of Operations Research

IS - 3

ER -

A Stochastic Representation for Nonlocal Parabolic PDEs with Applications

Abstract

Keywords

ASJC Scopus subject areas

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