摘要
This paper studies singular optimal control problems for systems described by nonlinear-controlled stochastic differential equations of mean-field type(MFSDEs in short),in which the coefficients depend on the state of the solution process as well as of its expected value.Moreover,the cost functional is also of mean-field type.The control variable has two components,the first being absolutely continuous and the second singular.We establish necessary as well as sufficient conditions for optimal singular stochastic control where the system evolves according to MFSDEs.These conditions of optimality differs from the classical one in the sense that here the adjoint equation turns out to be a linear mean-field backward stochastic differential equation.The proof of our result is based on convex perturbation method of a given optimal control.The control domain is assumed to be convex.A linear quadratic stochastic optimal control problem of mean-field type is discussed as an illustrated example.
基金
The authorwould like to thank the editor,the associate editor,and anonymous referees for their constructive corrections and valuable suggestions that improved the manuscript.The author was partially supported by Algerian PNR Project Grant 08/u07/857,ATRST-(ANDRU)2011-2013.
