First and second order necessary conditions for stochastic optimal controls

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:262

Article

Frankowska, Helene¹  Zhang, Haisen²  Zhang, Xu³ 

[1] Univ Paris Diderot, UPMC Univ Paris 06, Sorbonne Univ, CNRS,IMJ PRG,UMR 7586, Case 247,4 Pl Jussieu, F-75252 Paris, France

[2] Southwest Univ, Sch Math & Stat, Chongqing 400715, Peoples R China

[3] Sichuan Univ, Sch Math, Chengdu 610064, Peoples R China

关键词: Stochastic optimal control;    Malliavin calculus;    Necessary conditions;    Adjacent cone;    Variational equation;    Adjoint equation;   

DOI  :  10.1016/j.jde.2016.11.041

来源: Elsevier

【 摘 要 】

The main purpose of this paper is to establish the first and second order necessary optimality conditions for stochastic optimal controls using the classical variational analysis approach. The control system is governed by a stochastic differential equation, in which both drift and diffusion terms may contain the control variable and the set of controls is allowed to be nonconvex. Only one adjoint equation is introduced to derive the first order necessary condition; while only two adjoint equations are needed to state the second order necessary conditions for stochastic optimal controls. (C) 2016 Elsevier Inc. All rights reserved.

【 授权许可】

Free