Special weak Dirichlet processes and BSDEs driven by a random measure.

Elena Bandini and Francesco Russo

2018

Publication type:

Paper in peer-reviewed journals

Journal:

Bernoulli, vol. 24(4A), pp. 2569-2609

DOI:

10.3150/17-BEJ937

HAL:

hal-01241076

arXiv:

1512.06234

Keywords :

Random measure; Stochastic integrals for jump processes; Backward stochastic differential equations

Abstract:

This paper considers a forward BSDE driven by a random measure, when the underlying forward process $X$ is special semimartingale, or even more generally, a special weak Dirichlet process. Given a solution $(Y,Z,U)$, generally $Y$ appears to be of the type $u(t,X_t)$ where $u$ is a deterministic function. In this paper we identify $Z$ and $U$ in terms of $u$ applying stochastic calculus with respect to weak Dirichlet processes.

BibTeX:

@article{Ban-Rus-2018,
    author={Elena Bandini and Francesco Russo },
    title={Special weak Dirichlet processes and BSDEs driven by a random 
           measure. },
    doi={10.3150/17-BEJ937 },
    journal={Bernoulli },
    year={2018 },
    volume={24(4A) },
    pages={2569--2609},
}