BSDEs with random default time and their applications to default risk

TL;DR

This paper studies backward stochastic differential equations with random default times, establishing existence, uniqueness, and comparison results, and applies these to derive saddle-point strategies in default risk-related stochastic games.

Contribution

It introduces a new class of BSDEs with random default times, proving their well-posedness and applying them to default risk and game theory.

Findings

Unique solutions for BSDEs with default times established

Comparison theorem for solutions proved

Application to saddle-point strategies in stochastic games

Abstract

In this paper we are concerned with backward stochastic differential equations with random default time and their applications to default risk. The equations are driven by Brownian motion as well as a mutually independent martingale appearing in a defaultable setting. We show that these equations have unique solutions and a comparison theorem for their solutions. As an application, we get a saddle-point strategy for the related zero-sum stochastic differential game problem.