6533b861fe1ef96bd12c4e67

RESEARCH PRODUCT

$L_2$-variation of L\'{e}vy driven BSDEs with non-smooth terminal conditions

Alexander SteinickeChristel Geiss

subject

Statistics and Probability$L_{2}$-regularityPure mathematicsSmoothness (probability theory)Malliavin calculus010102 general mathematicsChaos expansionPoisson random measureFunction (mathematics)Lipschitz continuityMalliavin calculus01 natural sciencesLévy process010104 statistics & probabilityStochastic differential equationMathematics::ProbabilityLévy processesbackward stochastic differential equations0101 mathematicsL 2 -regularityBrownian motionMathematics - ProbabilityMathematics

description

We consider the $L_2$-regularity of solutions to backward stochastic differential equations (BSDEs) with Lipschitz generators driven by a Brownian motion and a Poisson random measure associated with a L\'{e}vy process $(X_t)_{t\in[0,T]}$. The terminal condition may be a Borel function of finitely many increments of the L\'{e}vy process which is not necessarily Lipschitz but only satisfies a fractional smoothness condition. The results are obtained by investigating how the special structure appearing in the chaos expansion of the terminal condition is inherited by the solution to the BSDE.

yearjournalcountryeditionlanguage
2016-05-01
10.3150/14-bej684http://arxiv.org/abs/1212.3420