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arXiv · 1608.03584

Forward-backward SDEs with jumps and classical solutions to nonlocal quasilinear parabolic PDEs

Evelina Shamarova·Rui Sá Pereira
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Abstract

We obtain an existence and uniqueness theorem for fully coupled forward-backward SDEs (FBSDEs) with jumps via the classical solution to the associated quasilinear parabolic partial integro-differential equation (PIDE), and provide the explicit form of the FBSDE solution. Moreover, we embed the associated PIDE into a suitable class of non-local quasilinear parabolic PDEs which allows us to extend the methodology of Ladyzhenskaya et al (1968) to non-local PDEs of this class. Namely, we obtain the existence and uniqueness of a classical solution to both the Cauchy problem and the initial-boundary value problem for non-local quasilinear parabolic second-order PDEs.

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Evelina Shamarova, Rui Sá Pereira. 2016-08-11. Forward-backward SDEs with jumps and classical solutions to nonlocal quasilinear parabolic PDEs. https://doi.org/10.1016/j.spa.2019.11.002

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