Discrete Time McKean–Vlasov Control Problem: A Dynamic Programming Approach

Journal Article · Thu Dec 15 00:00:00 EST 2016 · Applied Mathematics and Optimization

DOI:https://doi.org/10.1007/S00245-016-9386-9· OSTI ID:22617153

Pham, Huyên; Wei, Xiaoli ^[1]

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1. Laboratoire de Probabilités et Modèles Aléatoires, CNRS, UMR 7599, Université Paris Diderot (France)

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.

• OSTI ID: 22617153
• Journal Information: Applied Mathematics and Optimization, Vol. 74, Issue 3; Other Information: Copyright (c) 2016 Springer Science+Business Media New York; http://www.springer-ny.com; Country of input: International Atomic Energy Agency (IAEA); ISSN 0095-4616
• Country of Publication: United States
• Language: English

Related Subjects

97 MATHEMATICAL METHODS AND COMPUTING
DISTRIBUTION
DYNAMIC PROGRAMMING
MEAN-FIELD THEORY
MULTIVARIATE ANALYSIS
NONLINEAR PROBLEMS
OPTIMAL CONTROL
PROGRAMMING
STOCHASTIC PROCESSES