L2-variation of L\'evy driven BSDEs with non-smooth terminal conditions
Abstract
We consider the L2-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\'evy process (Xt)t∈[0,T]. The terminal condition may be a Borel function of finitely many increments of the L\'evy 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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