Martingale driven BSDEs, PDEs and other related deterministic problems

Adrien Barrasso and Francesco Russo

february, 2021

Publication type:

Paper in peer-reviewed journals

Journal:

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

DOI:

10.1016/j.spa.2020.11.007

HAL:

hal-01566883

arXiv:

1707.07879

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},
}