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A Stochastic Representation for Nonlocal Parabolic PDEs with Applications

Author

Listed:
  • 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)

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.

Suggested Citation

  • Min Dai & Steven Kou & Chen Yang, 2022. "A Stochastic Representation for Nonlocal Parabolic PDEs with Applications," Mathematics of Operations Research, INFORMS, vol. 47(3), pages 1707-1730, August.
    • Handle: RePEc:inm:ormoor:v:47:y:2022:i:3:p:1707-1730
    DOI: 10.1287/moor.2020.1061
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    References listed on IDEAS

    as
    1. Adams, A. T. & Clunie, J. B., 2006. "Risk Assessment Techniques for Split Capital Investment Trusts," Annals of Actuarial Science, Cambridge University Press, vol. 1(1), pages 7-36, March.
    2. repec:bla:jfinan:v:44:y:1989:i:5:p:1263-87 is not listed on IDEAS
    3. Abel Cadenillas & Peter Lakner & Michael Pinedo, 2010. "Optimal Control of a Mean-Reverting Inventory," Operations Research, INFORMS, vol. 58(6), pages 1697-1710, December.
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