6533b854fe1ef96bd12af560

RESEARCH PRODUCT

Existence, uniqueness and Malliavin differentiability of Lévy-driven BSDEs with locally Lipschitz driver

Christel GeissAlexander Steinicke

subject

Statistics and Probabilitymatematiikkalocally Lipschitz generatormalliavin differentiability of BSDEsMalliavin-laskentaexistence and uniqueness of solutions to BSDEsBSDEs with jumpsLipschitz continuityLévy processArticleStochastic differential equationMathematics::ProbabilityModeling and Simulationquadratic BSDEsApplied mathematics60H10UniquenessDifferentiable functiondifferentiaaliyhtälötMathematics - Probabilitystokastiset prosessitMathematics

description

We investigate conditions for solvability and Malliavin differentiability of backward stochastic differential equations driven by a L\'evy process. In particular, we are interested in generators which satisfy a locally 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 L\'evy-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 $\xi$ and its Malliavin derivative $D\xi$. 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.

yearjournalcountryeditionlanguage
2019-06-12
https://puretest.unileoben.ac.at/portal/en/publications/existence-uniqueness-and-malliavin-differentiability-of-levydriven-bsdes-with-locally-lipschitz-driver(b9977f99-ca17-471c-a3be-7427da0b69ff).html