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,Xt) 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.