A unified approach to a priori estimates for supersolutions of BSDEs in general filtrations

TL;DR

This paper develops a unified method for deriving a priori estimates for supersolutions of backward stochastic differential equations (BSDEs) in general filtrations, extending previous approaches by incorporating advanced supermartingale estimates.

Contribution

It introduces a novel unified approach that generalizes deep supermartingale estimates for BSDE supersolutions in non-quasi left-continuous filtrations.

Findings

Established well-posedness of reflected BSDEs in a broad framework.

Extended a priori estimates beyond classical settings.

Demonstrated applicability to complex filtration structures.

Abstract

We provide a unified approach to a priori estimates for supersolutions of BSDEs in general filtrations, which may not be quasi left-continuous. Unlike the previous related approaches in simpler settings, our results do not only rely on a simple application of It\^o's formula and classical estimates, but use crucially appropriate generalizations of deep estimates for supermartingales obtained by Meyer. As an example of application, we prove that reflected BSDEs are well-posed in a general framework which has not been covered so far in the existing literature.