CIRJE-F-997

"Quadratic-exponential Growth BSDEs with Jumps and Their Malliavin’s Differentiability"

Author Name

Fujii, Masaaki and Akihiko Takahashi

Date

December 2015

Full Paper   PDF file
Remarks  Revised in October 2016 and March 2017.
Abstract

We investigate a class of quadratic-exponential growth BSDEs with jumps. The quadratic structure introduced by Barrieu & El Karoui (2013) yields the universal bounds on the possible solutions. With local Lipschitz continuity and the so-called AΓ-condition for the comparison principle to hold, we prove the existence of a unique solution under the general quadratic-exponential structure. We have also shown that the strong convergence occurs under more general (not necessarily monotone) sequence of drivers, which is then applied to give the sufficient conditions for the Malliavin's differentiability.