Reflected Backward Stochastic Differential Equation with Rank-Based Data

Reflected Backward Stochastic Differential Equation with Rank-Based Data

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 BS...

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Veröffentlicht in:Journal of theoretical probability 2021-09, Vol.34 (3), p.1213-1247
Hauptverfasser: Chen, Zhen-Qing, Feng, Xinwei
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Mathematics
Mathematics and Statistics
Parabolic differential equations
Partial differential equations
Probability Theory and Stochastic Processes
Statistics
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description 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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subjects Mathematics
Mathematics and Statistics
Parabolic differential equations
Partial differential equations
Probability Theory and Stochastic Processes
Statistics
title Reflected Backward Stochastic Differential Equation with Rank-Based Data
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