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Existence, uniqueness and Malliavin differentiability of Lévy-driven BSDEs with locally Lipschitz driver
Christel Geiss1, Alexander Steinicke2
1Department of Mathematics and Statistics, University of Jyvaskyla, Jyvaskyla, Finland.
Abstract:
We investigate conditions for solvability and Malliavin differentiability of backward stochastic differential equations driven by a Lévy process. In particular, we are interested in generators which satisfy a local Lipschitz condition in the Z and U variable. This includes settings of linear, quadratic and exponential growths in those variables. Extending an idea of Cheridito and Nam to the jump setting and applying comparison theorems for Lévy-driven BSDEs, we show existence, uniqueness, boundedness and Malliavin differentiability of a solution. The pivotal assumption to obtain these results is a boundedness condition on the terminal value ξ and its Malliavin derivative . Furthermore, we extend existence and uniqueness theorems to cases where the generator is not even locally Lipschitz in U. BSDEs of the latter type find use in exponential utility maximization.
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