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

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  • Shamarova, Evelina
  • Sá Pereira, Rui

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.

Suggested Citation

  • Shamarova, Evelina & Sá Pereira, Rui, 2020. "Forward–backward SDEs with jumps and classical solutions to nonlocal quasilinear parabolic PDEs," Stochastic Processes and their Applications, Elsevier, vol. 130(7), pages 3865-3894.
    • Handle: RePEc:eee:spapps:v:130:y:2020:i:7:p:3865-3894
    DOI: 10.1016/j.spa.2019.11.002
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    References listed on IDEAS

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    1. Cruzeiro, Ana Bela & Shamarova, Evelina, 2009. "Navier-Stokes equations and forward-backward SDEs on the group of diffeomorphisms of a torus," Stochastic Processes and their Applications, Elsevier, vol. 119(12), pages 4034-4060, December.
    2. Li, Juan & Wei, Qingmeng, 2014. "Lp estimates for fully coupled FBSDEs with jumps," Stochastic Processes and their Applications, Elsevier, vol. 124(4), pages 1582-1611.
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