Reflected Backward Stochastic Differential Equation with Rank-Based Data

Zhen-Qing Chen () and Xinwei Feng ()
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Zhen-Qing Chen: University of Washington
Xinwei Feng: Shandong University

Journal of Theoretical Probability, 2021, vol. 34, issue 3, 1213-1247

Abstract: 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.

Keywords: Reflected backward stochastic differential equation; Rank-based coefficients; Obstacle problem; Partial differential equation; Viscosity solution; Primary 60H10; 60H30; Secondary 35K85 (search for similar items in EconPapers)
Date: 2021
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s10959-020-01026-9

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