Martingale driven BSDEs, PDEs and other related deterministic problems

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:133

Article

Barrasso, Adrien¹  Russo, Francesco² 

[1] Univ Evey Val Essonne, Lab Math & Modelisat, 23 Bd France, F-91037 Evry, France

[2] ENSTA Paris, Inst Polytech Paris, Unite Math Appl, 828 Blvd Marechaux, F-91120 Palaiseau, France

关键词: Decoupled mild solutions;    Martingale problem;    Cadlag martingale;    Pseudo-PDE;    Markov processes;    Backward stochastic differential equation;   

DOI  :  10.1016/j.spa.2020.11.007

来源: Elsevier

【 摘 要 】

We focus on a class of BSDEs driven by a cadlag martingale and the corresponding Markovian BSDEs which arise when the randomness of the driver appears through a Markov process. To those BSDEs we associate a deterministic equation which, when the Markov process is a Brownian diffusion, is nothing else but a parabolic semi-linear PDE. We prove existence and uniqueness of a decoupled mild solution of the deterministic problem, and give a probabilistic representation of this solution through the aforementioned BSDEs. (C) 2020 Elsevier B.V. All rights reserved.

【 授权许可】

Free