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

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:130

Article

Shamarova, Evelina¹  Pereira, Rui Sa² 

[1] Univ Fed Paraiba, Dept Matemat, Joao Pessoa, Paraiba, Brazil

[2] Univ Porto, Dept Matemat, Rua Campo Alegre, Porto, Portugal

关键词: Forward-backward SDEs with jumps;    Non-local quasilinear parabolic PDEs;    Partial integro-differential equations;   

DOI  :  10.1016/j.spa.2019.11.002

来源: Elsevier

【 摘 要 】

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. (C) 2019 Elsevier B.V. All rights reserved.

【 授权许可】

Free