Doubly Reflected BSDEs with default time under stochastic Lipschitz coefficients and Applications

TL;DR

This paper introduces a new class of doubly reflected backward stochastic differential equations with default time, proving their existence and uniqueness, and applies them to a generalized Dynkin game with saddle point existence.

Contribution

It develops a novel formulation of doubly reflected BSDEs with default time and separated barriers, and links them to a generalized Dynkin game in a defaultable setting.

Findings

Existence and uniqueness of solutions for the proposed BSDEs.

Characterization of the game value via BSDE solutions.

Proof of saddle point existence in the generalized Dynkin game.

Abstract

We formulate a notion of doubly reflected BSDEs with a default time and two completely separated RCLL barriers. We demonstrate the existence and uniqueness of the solution. Within the defaultable setup, we introduce a type of generalized Dynkin game, we characterize the common value of the game via the solution of the doubly reflected BSDEs and we show the existence of a saddle point.