Martingale driven BSDEs, PDEs and other related deterministic problems

We focus on a class of BSDEs driven by a càdlàg 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 els...

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Bibliographic Details
Published in:Stochastic processes and their applications 2021-03, Vol.133, p.193-228
Main Authors: Barrasso, Adrien, Russo, Francesco
Format: Article
Language:English
Subjects:
Backward stochastic differential equation
Càdlàg martingale
Decoupled mild solutions
Markov processes
Martingale problem
Mathematics
Probability
Pseudo-PDE
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Summary:We focus on a class of BSDEs driven by a càdlàg 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.
ISSN:0304-4149
1879-209X
DOI:10.1016/j.spa.2020.11.007