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

Document Type : Research Article

Authors

Laboratory of Mathematical Analysis, Probability and Optimizations, Department of Mathematics, University of Biskra, PO Box 145, Biskra 7000, Algeria

Abstract

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.

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Journal of Mathematical Modeling
Volume 12, Issue 3
September 2024
Pages 517-532

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