Applied Mathematics and Optimization, Vol.74, No.3, 487-506, 2016
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.