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Reflected Backward Stochastic Differential Equation with Rank-Based Data

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  • Zhen-Qing Chen

    (University of Washington)

  • Xinwei Feng

    (Shandong University)

Abstract

In this paper, we study reflected backward stochastic differential equation (reflected BSDE) with rank-based data in a Markovian framework; that is, the solution to the reflected BSDE is above a prescribed boundary process in a minimal fashion and the generator and terminal value of the reflected BSDE depend on the solution of another stochastic differential equation (SDE) with rank-based drift and diffusion coefficients. We derive regularity properties of the solution to such reflected BSDE and show that the solution at the initial starting time t and position x, which is a deterministic function, is the unique viscosity solution to some obstacle problem (or variational inequality) for the corresponding parabolic partial differential equation.

Suggested Citation

  • Zhen-Qing Chen & Xinwei Feng, 2021. "Reflected Backward Stochastic Differential Equation with Rank-Based Data," Journal of Theoretical Probability, Springer, vol. 34(3), pages 1213-1247, September.
    • Handle: RePEc:spr:jotpro:v:34:y:2021:i:3:d:10.1007_s10959-020-01026-9
    DOI: 10.1007/s10959-020-01026-9
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    References listed on IDEAS

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    1. Banner, Adrian D. & Ghomrasni, Raouf, 2008. "Local times of ranked continuous semimartingales," Stochastic Processes and their Applications, Elsevier, vol. 118(7), pages 1244-1253, July.
    2. Jin Ma & Jakša Cvitanić, 2001. "Reflected forward-backward SDE s and obstacle problems with boundary conditions," International Journal of Stochastic Analysis, Hindawi, vol. 14, pages 1-26, January.
    3. N. El Karoui & S. Peng & M. C. Quenez, 1997. "Backward Stochastic Differential Equations in Finance," Mathematical Finance, Wiley Blackwell, vol. 7(1), pages 1-71, January.
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