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May 2016 $L_{2}$-variation of Lévy driven BSDEs with non-smooth terminal conditions
Christel Geiss, Alexander Steinicke
Bernoulli 22(2): 995-1025 (May 2016). DOI: 10.3150/14-BEJ684


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 Lévy process $(X_{t})_{t\in[0,T]}$. The terminal condition may be a Borel function of finitely many increments of the Lévy 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.


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Christel Geiss. Alexander Steinicke. "$L_{2}$-variation of Lévy driven BSDEs with non-smooth terminal conditions." Bernoulli 22 (2) 995 - 1025, May 2016.


Received: 1 December 2012; Revised: 1 October 2014; Published: May 2016
First available in Project Euclid: 9 November 2015

zbMATH: 1335.60089
MathSciNet: MR3449806
Digital Object Identifier: 10.3150/14-BEJ684

Keywords: $L_{2}$-regularity , Backward stochastic differential equations , chaos expansion , Lévy processes , Malliavin calculus

Rights: Copyright © 2016 Bernoulli Society for Mathematical Statistics and Probability

Vol.22 • No. 2 • May 2016
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