Markovian quadratic and superquadratic BSDEs with an unbounded terminal condition

TL;DR

This paper establishes existence and uniqueness results for quadratic and superquadratic Markovian BSDEs with unbounded terminal conditions, linking these to PDE solutions and providing convergence rates for numerical approximations.

Contribution

It introduces a strong a priori estimate on Z that enables solving BSDEs with unbounded terminal conditions and quadratic or superquadratic growth, advancing the theoretical understanding.

Findings

Proves existence and uniqueness of solutions for quadratic and superquadratic BSDEs.

Provides explicit convergence rates for time discretization of these BSDEs.

Links BSDE solutions to viscosity solutions of semilinear PDEs.

Abstract

This article deals with the existence and the uniqueness of solutions to quadratic and superquadratic Markovian backward stochastic differential equations (BSDEs for short) with an unbounded terminal condition. Our results are deeply linked with a strong a priori estimate on $Z$ that takes advantage of the Markovian framework. This estimate allows us to prove the existence of a viscosity solution to a semilinear parabolic partial differential equation with nonlinearity having quadratic or superquadratic growth in the gradient of the solution. This estimate also allows us to give explicit convergence rates for time approximation of quadratic or superquadratic Markovian BSDEs.