What question did this study set out to answer?

To explore a new class of reflected BSDEs incorporating jumps and default times, and their applications in financial contexts.

April 24, 2026

On Reflected Bsdes With Jumps and Default Time

Key Points

To explore a new class of reflected BSDEs incorporating jumps and default times, and their applications in financial contexts.
Introduced a stochastic framework integrating Brownian motion and integer-valued random measures.
Proved existence and uniqueness of solutions under stochastic Lipschitz conditions.
Examined connections to optimal stopping problems and American option pricing in defaultable markets.
Established the well-posedness of the proposed reflected BSDEs.
Identified relations between the BSDEs and dynamic risk measures.
Presented methods for pricing and hedging American options in markets with jumps.

Abstract

We introduce a new class of reflected BSDEs with default times and irregular obstacles, where the publicly available information is generated by a Brownian motion and an independent integer-valued random measure. Under a stochastic Lipschitz condition on the driver, we establish the well-posedness of the problem by proving the existence and uniqueness of a solution. As an application, we investigate the connection between these equations and optimal stopping problems with dynamic risk measures defined via nonlinear expectations, as well as the pricing and hedging of American options in a general defaultable market with jumps.

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