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Discrete time McKean-Vlasov control problem: a dynamic programming approach (1511.09273v1)
Published 30 Nov 2015 in math.PR and math.OC
Abstract: 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.