Reflected Backward Stochastic Differential Equation with Rank-Based Data

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.