"Quadratic-exponential Growth BSDEs with Jumps and Their Malliavin’s Differentiability"
Fujii, Masaaki and Akihiko Takahashi
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|Remarks||Revised in October 2016, March and September 2017; forthcoming in Stochastic Processes and their Applications.|
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.