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arXiv · 1212.3420

$L_2$-variation of Lévy driven BSDEs with non-smooth terminal conditions

Christel Geiss·Alexander Steinicke
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Abstract

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. 2016-02-15. $L_2$-variation of Lévy driven BSDEs with non-smooth terminal conditions. https://doi.org/10.3150/14-bej684

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