A Mean-Field Necessary and Sufficient Conditions for Optimal Singular Stochastic Control

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• 作者：Mokhtar Hafayed (1)
  
• 关键词：Stochastic optimal singular control ; Mean ; field stochastic maximum principle ; Mean ; field necessary and sufficient conditions of optimality ; McKean鈥揤lasov SDEs ; Convex perturbation ; 60H10 ; 93E20
• 刊名：Communications in Mathematics and Statistics
• 出版年：2013
• 出版时间：December 2013
• 年：2013
• 卷：1
• 期：4
• 页码：417-435
• 全文大小：208 KB
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• 作者单位：Mokhtar Hafayed (1)
  
  1. Laboratory of Applied Mathematics, Biskra University, PO Box 145, 07000聽, Biskra, Algeria
  
• ISSN：2194-671X

文摘

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.