Reflected Backward Stochastic Differential Equation with Rank-based Data

Zhen-Qing Chen; Xinwei Feng

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arXiv · 2007.05886

Reflected Backward Stochastic Differential Equation with Rank-based Data

Zhen-Qing Chen·Xinwei Feng

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Abstract

In this paper, we study reflected backward stochastic differential equation (reflected BSDE in abbreviation) 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 in abbreviation) 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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BibTeX RIS

Zhen-Qing Chen, Xinwei Feng. 2020-07-12. Reflected Backward Stochastic Differential Equation with Rank-based Data. https://arxiv.org/abs/2007.05886

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