Re ected and Doubly Re ected BSDEs with Jumps: A Priori Estimates and Comparison

It is now established that under quite general circumstances, including in models with jumps, existence of a solution to a re ected BSDE is guaranteed under mild conditions, whereas existence of a solution to a doubly re ected BSDE is essentially equivalent to the so-called Mokobodski condition. As for uniqueness of solutions, it holds under mild integrability conditions. However, for practical purposes, existence and uniqueness is not enough. In order to give further developments to these results in Markovian set-ups, one also need a (simply or doubly) re ected BSDE to be wellposed, in the sense that the solution satis es 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 on a pricing problem in nance.