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Singular optimal control problems with recursive utilities of mean‐field type
Author(s) -
Hao Tao,
Meng Qingxin
Publication year - 2021
Publication title -
asian journal of control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.769
H-Index - 53
eISSN - 1934-6093
pISSN - 1561-8625
DOI - 10.1002/asjc.2307
Subject(s) - mathematics , optimal control , mean field theory , stochastic differential equation , singular control , singular solution , mathematical optimization , field (mathematics) , stochastic control , maximum principle , order (exchange) , control (management) , type (biology) , matrix (chemical analysis) , control theory (sociology) , mathematical analysis , computer science , pure mathematics , ecology , physics , finance , quantum mechanics , artificial intelligence , economics , biology , materials science , composite material
In this paper a second‐order necessary condition for singular optimal controls with recursive utilities of mean‐field control systems is investigated. For our mean‐field singular control problem, the second‐order adjoint system is not a single mean‐field backward stochastic differential equation (BSDE), but a matrix‐valued system, which consists of three classical BSDEs. Based on this observation, a new second‐order expansion of cost functionalY εis proved and also the stochastic maximum principle. Our method is appropriate for a large class of mean‐field singular optimal control problems.