Stochastic Quadratic BSDE With Two RCLL Obstacles

TL;DR

This paper establishes the existence of maximal solutions for generalized backward stochastic differential equations with two right-continuous, left-limited obstacles under weak conditions, including stochastic quadratic growth and without P-integrability assumptions.

Contribution

It proves the existence of solutions for GRBSDEs with weaker assumptions on data and barriers, extending previous results to more general settings.

Findings

Existence of maximal solutions under weaker assumptions.

Solutions accommodate stochastic quadratic growth in z.

Barriers are only right continuous and left limited.

Abstract

We study the problem of existence of solutions for generalized backward stochastic differential equation with two reflecting barriers (GRBSDE for short) under weaker assumptions on the data. Roughly speaking we show the existence of a maximal solution for GRBSDE when the terminal condition \xi is F_T-measurable, the coefficient f is continuous with general growth with respect to the variable y and stochastic quadratic growth with respect to the variable z and the reflecting barriers L and U are just right continuous left limited. The result is proved without assuming any P-integrability conditions.