Backward stochastic differential equations with stopping time as time horizon

TL;DR

This paper introduces a novel method for analyzing backward stochastic differential equations with stopping times as the time horizon, extending existing results from fixed to random time horizons.

Contribution

The paper presents a new approach for studying BSDEs with stopping times, generalizing results from constant to random time horizons.

Findings

Generalization of BSDE results to random time horizons

Introduction of a new analytical method for BSDEs with stopping times

Extension of classical BSDE theory to stochastic time horizons

Abstract

In this paper, we introduce a new method for study on backward stochastic differential equations with stopping time as time horizon. And using this, we show that some results on backward stochastic differential equations with constant time horizon are generalized to the case of random time horizon.