Martingale driven BSDEs, PDEs and other related deterministic problems
february, 2021
Publication type:
Paper in peer-reviewed journals
Journal:
Stochastic Processes and their Applications, vol. 133, 193-228
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Keywords :
Decoupled mild solutions; Martingale problem; cadlag martingale; pseudo-PDE; Markov processes; backward stochastic differential equation.
Abstract:
We focus on a class of BSDEs driven by a cadlag martingale and corresponding Markov type BSDE which arise when the randomness of the driver appears through a Markov process. To those BSDEs we associate a deterministic problem which, when the Markov process is a Brownian diffusion, is nothing else but a parabolic type PDE. The solution of the deterministic problem is intended as decoupled mild solution, and it is formulated with the help of a time-inhomogeneous semigroup.
BibTeX:
@article{Bar-Rus-2021, author={Adrien Barrasso and Francesco Russo }, title={Martingale driven BSDEs, PDEs and other related deterministic problems }, doi={10.1016/j.spa.2020.11.007 }, journal={Stochastic Processes and their Applications, vol. 133, 193-228 }, year={2021 }, month={2}, }