Special weak Dirichlet processes and BSDEs driven by a random measure

Abstract

This paper considers a forward BSDE driven by a random measure, when the underlying forward process $X$ is a 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.