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

By St'ephane Cr'epey, Anis Matoussi. 2008

126 citations recorded by the source corpus.

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.

Subfields: Economics and Econometrics, Finance, Management Science and Operations Research

View Paper: https://www.semanticscholar.org/paper/0757873e464534c307b4aae0d36cdab77b4e9b46

Citations in the corpus

• Generalized Dynkin games and doubly reflected BSDEs with jumps (2013, unknown): “A comparison theorem has been provided in [7] in the case of jumps under stronger assumptions, with a different proof based on Itô’s calculus.”