Stochastic maximum principle for generalized mean-field delay control problem

Hancheng Guo; Jie Xiong; Jiayu Zheng

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arXiv · 1708.03622

Stochastic maximum principle for generalized mean-field delay control problem

Hancheng Guo·Jie Xiong·Jiayu Zheng

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Abstract

In this paper, we first give the existence and uniqueness theorems for generalized mean-filed delay stochastic differential equations (GMFDSDEs) and mean-field anticipated backward stochastic differential equations (MFABSDEs). Then we study the stochastic maximum principle for generalized mean-filed delay control problem. Since the state is distribution-depending, we define the adjoint equation as a MFABSDE, in which, all the derivatives of coefficients are in Fr\'echet sense. We deduce the stochastic maximum principle, and also obtain, under some additional assumptions, a sufficient condition for the optimality of the control.

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BibTeX RIS

Hancheng Guo, Jie Xiong, Jiayu Zheng. 2017-08-10. Stochastic maximum principle for generalized mean-field delay control problem. https://arxiv.org/abs/1708.03622

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