Lp Solutions of Quadratic BSDEs

TL;DR

This paper investigates quadratic backward stochastic differential equations with Lp terminal conditions, providing new estimates, existence, uniqueness, and stability results, and linking solutions to quadratic PDEs.

Contribution

It extends the quadratic BSDE literature by weakening assumptions and establishing comparison, uniqueness, and stability results using the { heta}-technique.

Findings

Established Lp-type estimates for quadratic BSDEs.

Proved existence and uniqueness under weak assumptions.

Connected BSDE solutions to viscosity solutions of quadratic PDEs.

Abstract

We study a general class of quadratic BSDEs with terminal value in Lp for p > 1. First of all, we give an Lp-type estimate and existence result. Under the additional assumption of monotonicity and convexity, we derive the comparison theorem, uniqueness and stability result via {\theta}-technique (Briand and Hu [7]). The assumptions employed throughout this paper are rather weak and extend the quadratic BSDE literature. Finally, a probabilistic representation for the viscosity solution to the associated quadratic PDEs is given.