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June  2018, 8(2): 451-473. doi: 10.3934/mcrf.2018018

## A second-order stochastic maximum principle for generalized mean-field singular control problem

 Department of Mathematics, Faculty of Science and Technology, University of Macau, Macau, 999078, China

* Corresponding author: Hancheng Guo

Received  April 2017 Revised  October 2017 Published  March 2018

Fund Project: Research supported partially by FDCT 025/2016/A1.

In this paper, we study the generalized mean-field stochastic control problem when the usual stochastic maximum principle (SMP) is not applicable due to the singularity of the Hamiltonian function. In this case, we derive a second order SMP. We introduce the adjoint process by the generalized mean-field backward stochastic differential equation. The keys in the proofs are the expansion of the cost functional in terms of a perturbation parameter, and the use of the range theorem for vector-valued measures.

Citation: Hancheng Guo, Jie Xiong. A second-order stochastic maximum principle for generalized mean-field singular control problem. Mathematical Control & Related Fields, 2018, 8 (2) : 451-473. doi: 10.3934/mcrf.2018018
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