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

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.

preprint2015arXivOpen access
Huyên PhamXiaoli Wei
math.OCmath.PR
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Huyên PhamXiaoli Wei

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