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

2017/04/26 by Hancheng Guo, Jie Xiong, Guo, Hancheng +1 · 1 citation
Decision Sciences · Economics, Econometrics and Finance · Mathematics · Social Sciences · #60H30 #70G70 #93E03 #93E20 #FOS: Mathematics #Insurance, Mortality, Demography, Risk Management #Optimization and Control (math.OC) #Risk and Portfolio Optimization #Stochastic processes and financial applications #math.OC #msc:60H30 #msc:70G70 #msc:93E03 #msc:93E20

paper · pdf · doi:10.48550/arxiv.1704.08002

22pages

arxiv created 2017/04/26 · openalex publication_date 2017/04/26 · arxiv updated 2017/04/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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.

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