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Reflected Backward Stochastic Differential Equation with Rank-Based Data

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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.

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Acknowledgements

The authors thank the anonymous referee for helpful comments that led to the improvement of the exposition of this paper.

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Authors and Affiliations

  1. Department of Mathematics, University of Washington, Seattle, WA, 98195, USA

    Zhen-Qing Chen

  2. Zhongtai Securities Institute for Financial Studies, Shandong University, **an, 250100, Shandong, China

    **nwei Feng

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  1. Zhen-Qing Chen
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  2. **nwei Feng
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Correspondence to **nwei Feng.

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Zhen-Qing Chen: Research was supported in part by Simons Foundation Grant 520542 and Victor Klee Faculty Fellowship at UW.

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Chen, ZQ., Feng, X. Reflected Backward Stochastic Differential Equation with Rank-Based Data. J Theor Probab 34, 1213–1247 (2021). https://doi.org/10.1007/s10959-020-01026-9

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  • DOI: https://doi.org/10.1007/s10959-020-01026-9

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