Skorohod Equation and Reflected Backward Stochastic Differential Equations

TL;DR

This paper introduces a novel iterative approach based on the Skorohod equation for solving a class of reflected backward stochastic differential equations with non-linear resistance, enhancing the methodology for studying these equations.

Contribution

The paper presents a new method utilizing the Skorohod equation to solve reflected BSDEs with non-linear resistance, improving upon previous approaches.

Findings

Developed an iteration procedure for reflected BSDEs

Applied the method to equations with non-linear resistance

Provided a new perspective on reflected BSDEs

Abstract

By using the Skorohod equation we derive an iteration procedure which allows us to solve a class of reflected backward stochastic differential equations with non-linear resistance induced by the reflected local time. In particular, we present a new method to study the reflected BSDE proposed first by El Karoui et al. \cite{MR1434123}.