Uniqueness of Solutions for Certain Markovian Backward Stochastic Differential Equations

TL;DR

This paper proves the uniqueness of solutions for a class of Markovian backward stochastic differential equations (BSDEs) and their related nonlinear PDEs, using probabilistic methods and illustrating with a control application.

Contribution

It establishes the uniqueness of solutions for Markovian BSDEs linked to nonlinear PDEs, leveraging probabilistic interpretation, which was not previously demonstrated.

Findings

Uniqueness of solutions for Markovian BSDEs is proven.

The approach connects BSDE solutions to nonlinear PDEs.

An example of a stochastic control application is provided.

Abstract

This paper considers the problem of uniqueness of the solutions to a class of Markovian backward stochastic differential equations (BSDEs) which are also connected to certain nonlinear partial differential equation (PDE) through a probabilistic representation. Assuming that there is a solution to the BSDE or to the corresponding PDE, we use the probabilistic interpretation to show the uniqueness of the solutions, and provide an example of a stochastic control application.