Special weak Dirichlet processes and BSDEs driven by a random measure

Elena Bandini (1, 2) , Francesco Russo (2, 3)

1 POLIMI - Politecnico di Milano [Milan]
2 UMA - Unité de Mathématiques Appliquées
3 OC - Optimisation et commande

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.

Mots clés: Weak Dirichlet processes; Calculus via regularizations; Random measure; Stochastic integrals for jump processes; Backward stochastic differential equations

Domaines: Probabilités [math.PR]

Elena Bandini, Francesco Russo. Special weak Dirichlet processes and BSDEs driven by a random measure. Bernoulli, 2018, 24 (4A), pp.2569-2609. ⟨10.3150/17-BEJ937⟩. ⟨hal-01241076v2⟩