Lions's partial derivatives with respect to probability measures for general mean-field stochastic control problem

In this paper, a necessary stochastic maximum principle for stochastic model governed by mean-field nonlinear controlled It\rm{\ddot{o}}-stochastic differential equations is proved. The coefficients of our model are nonlinear and depend explicitly on the control variable, the state process as well as of its probability distribution. The control region is assumed to be bounded and convex. Our main result is derived by applying the Lions's partial-derivatives with respect to random measures in Wasserstein space. The associated It\rm{\ddot{o}}-formula and convex-variation approach are applied to establish the optimal control.

کلیدواژه ها:

Stochastic mean-field models ، stochastic control ، Lions's partial-derivatives with respect to measures ، maximum principle ، probability measure