Martingale driven BSDEs, PDEs and other related deterministic problems

Adrien Barrasso and Francesco Russo

Stochastic Processes and their Applications, 2021, vol. 133, issue C, 193-228

Abstract: 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.

Keywords: Decoupled mild solutions; Martingale problem; Càdlàg martingale; Pseudo-PDE; Markov processes; Backward stochastic differential equation (search for similar items in EconPapers)
Date: 2021
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Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:133:y:2021:i:c:p:193-228

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DOI: 10.1016/j.spa.2020.11.007

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