Generalized Snell Envelope as a Minimal Solution of BSDE With Lower Barriers

TL;DR

This paper characterizes the Snell envelope of a process as the minimal solution to a BSDE with lower barriers, establishing existence and uniqueness of this solution.

Contribution

It introduces a novel characterization of the Snell envelope via BSDEs with lower barriers, extending the theoretical framework for stochastic processes.

Findings

The minimal solution to the BSDE exists and is unique.

The Snell envelope can be represented as a solution to a BSDE with lower barriers.

Provides a new theoretical foundation for stochastic process optimization.

Abstract

The aim of this paper is to characterize the Snell envelope of a given P-measurable process l as the minimal solution of some backward stochastic differential equation with lower general reflecting barriers and to prove that this minimal solution exists.