Discrete time McKean-Vlasov control problem: a dynamic programming approach

Huyên Pham (1, 2) , Xiaoli Wei (1)

1 LPMA - Laboratoire de Probabilités et Modèles Aléatoires
2 CREST - Centre de Recherche en Économie et Statistique

We consider the stochastic optimal control problem of nonlinear mean-field systems in discrete time. We reformulate the problem into a deterministic control problem with marginal distribution as controlled state variable, and prove that dynamic programming principle holds in its general form. We apply our method for solving explicitly the mean-variance portfolio selection and the multivariate linear-quadratic McKean-Vlasov control problem.

Mots clés: Discrete time McKean-Vlasov equation; dynamic programming; calculus of variations

Domaines: Probabilités [math.PR]; Optimisation et contrôle [math.OC]

Huyên Pham, Xiaoli Wei. Discrete time McKean-Vlasov control problem: a dynamic programming approach. 2015. ⟨hal-01235234⟩