Probabilistic interpretation of a coupled system of Hamilton-Jacobi-Bellman equations

Rainer Buckdahn (1) , Ying Hu (2)

1 LM - Laboratoire de mathématiques de Brest
2 IRMAR - Institut de Recherche Mathématique de Rennes

In this paper, we give a probabilistic interpretation for a coupled system of Hamilton-Jacobi-Bellman equations using the value function of a stochastic control problem. First we introduce this stochastic control problem. Then we prove that the value function of this problem is deterministic and satisfies a (strong) dynamic programming principle. And finally, the value function is shown to be the unique viscosity solution of the coupled system of Hamilton-Jacobi-Bellman equations.

Mots clés: differential equations

Domaines: Probabilités [math.PR]

Rainer Buckdahn, Ying Hu. Probabilistic interpretation of a coupled system of Hamilton-Jacobi-Bellman equations. Journal of Evolution Equations, 2010, 10 (3), pp.529-549. ⟨10.1007/s00028-010-0060-4⟩. ⟨hal-00536262⟩