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

Evelina Shamarova and Rui Sá Pereira

Stochastic Processes and their Applications, 2020, vol. 130, issue 7, 3865-3894

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.

Keywords: Forward–backward SDEs with jumps; Non-local quasilinear parabolic PDEs; Partial integro-differential equations (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1016/j.spa.2019.11.002

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