L$^{p}$-solution of reflected generalized BSDEs with non-Lipschitz coefficients

TL;DR

This paper establishes existence and uniqueness results for reflected generalized backward stochastic differential equations with non-Lipschitz coefficients, advancing the mathematical theory of stochastic processes with reflections.

Contribution

It introduces new techniques in stochastic calculus to handle non-Lipschitz coefficients in RGBSDEs, extending prior results that required Lipschitz conditions.

Findings

Proved existence of solutions under non-Lipschitz conditions

Established uniqueness of solutions for reflected RGBSDEs

Developed new stochastic calculus methods for these equations

Abstract

In this paper, we continue in solving reflected generalized backward stochastic differential equations (RGBSDE for short) and fixed terminal time with use some new technical aspects of the stochastic calculus related to the reflected generalized BSDE. Here, existence and uniqueness of solution is proved under a non-Lipschitz condition on the coefficients.