A Class of Finite-Dimensional Numerically Solvable McKean-Vlasov Control Problems

Alessandro Balata (1) , Côme Huré (2) , Mathieu Laurière (3) , Huyên Pham (2) , Isaque Pimentel (4)

1 School of Mathematics [Leeds]
2 LPSM (UMR_8001) - Laboratoire de Probabilités, Statistique et Modélisation
3 NYU–ECNU Institute of Mathematical Sciences at NYU Shanghai
4 CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique

We address a class of McKean-Vlasov (MKV) control problems with common noise, called polynomial conditional MKV, and extending the known class of linear quadratic stochastic MKV control problems. We show how this polynomial class can be reduced by suitable Markov embedding to finite-dimensional stochastic control problems, and provide a discussion and comparison of three probabilistic numerical methods for solving the reduced control problem: quantization, regression by control randomization, and regress later methods. Our numerical results are illustrated on various examples from portfolio selection and liquidation under drift uncertainty, and a model of interbank systemic risk with partial observation.

Mots clés: McKean-Vlasov control; Regress later; Control randomization; polynomial class; quantization; regress-later; control randomization ˚

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

Alessandro Balata, Côme Huré, Mathieu Laurière, Huyên Pham, Isaque Pimentel. A Class of Finite-Dimensional Numerically Solvable McKean-Vlasov Control Problems. 2018. ⟨hal-01718751v2⟩