We investigate a class of quadratic-exponential growth BSDEs with jumps. The quadratic structure introduced by Barrieu & El Karoui (2013) yields the universal bound on the possible solutions. With a bounded terminal condition and local Lipschitz continuity , we give a simple and streamlined proof for the existence as well as the uniqueness of the solution without using the comparison principle. The properties of locally Lipschitz BSDEs with coefficients in BMO space enable us to show the  strong convergence of a sequence of globally Lipschitz BSDEs to the interested one , which is then used to give sufficient conditions for the Malliavin's differentiability.
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 A_gamma-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.
R
bound
bounds
D
a bounded terminal condition and
R
, we give a simple and streamlined proof for the existence as well as the uniqueness of the solution without using the comparison principle. The properties of locally Lipschitz BSDEs with coefficients in BMO space enable us to show
and
A
so-called A_gamma-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
R
of a sequence of globally Lipschitz BSDEs to the interested one
occurs under more general (not necessarily monotone) sequence of drivers
R
used to give
applied to give the