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

  • * Corresponding author: Hancheng Guo

    * Corresponding author: Hancheng Guo 
Research supported partially by FDCT 025/2016/A1.
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  • 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.

    Mathematics Subject Classification: Primary: 93E20, 93E03, 60H30; Secondary: 70G70.

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