Reflected and doubly reflected BSDEs with jumps: a priori estimates and comparison

TL;DR

This paper establishes a priori estimates and comparison theorems for reflected and doubly reflected BSDEs with jumps, enhancing their theoretical understanding and practical applicability, especially in financial pricing models.

Contribution

It provides new bounds, error estimates, and comparison results for reflected BSDEs with jumps, extending their theoretical framework and practical utility.

Findings

Derived a priori estimates for solutions

Established comparison theorems for reflected BSDEs

Applied results to a financial pricing problem

Abstract

It is now established that under quite general circumstances, including in models with jumps, the existence of a solution to a reflected BSDE is guaranteed under mild conditions, whereas the existence of a solution to a doubly reflected BSDE is essentially equivalent to the so-called Mokobodski condition. As for uniqueness of solutions, this holds under mild integrability conditions. However, for practical purposes, existence and uniqueness are not enough. In order to further develop these results in Markovian set-ups, one also needs a (simply or doubly) reflected BSDE to be well posed, in the sense that the solution satisfies suitable bound and error estimates, and one further needs a suitable comparison theorem. In this paper, we derive such estimates and comparison results. In the last section, applicability of the results is illustrated with a pricing problem in finance.