Linear quadratic optimal control of conditional McKean-Vlasov equation with random coefficients and applications *

Huyên Pham (1, 2)

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

We consider the optimal control problem for a linear conditional McKean-Vlasov equation with quadratic cost functional. The coefficients of the system and the weigh-ting matrices in the cost functional are allowed to be adapted processes with respect to the common noise filtration. Semi closed-loop strategies are introduced, and following the dynamic programming approach in [32], we solve the problem and characterize time-consistent optimal control by means of a system of decoupled backward stochastic Riccati differential equations. We present several financial applications with explicit solutions, and revisit in particular optimal tracking problems with price impact, and the conditional mean-variance portfolio selection in incomplete market model.

Mots clés: Stochastic McKean-Vlasov SDEs; random coefficients; linear quadratic op-timal control; dynamic programming; Riccati equation; backward stochastic differential equation

Domaines: Probabilités [math.PR]; Optimisation et contrôle [math.OC]; Finance quantitative [q-fin.CP]

Huyên Pham. Linear quadratic optimal control of conditional McKean-Vlasov equation with random coefficients and applications *. 2016. ⟨hal-01305929v1⟩