2018
DOI: 10.1002/oca.2403
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On optimal singular control problem for general Mckean‐Vlasov differential equations: Necessary and sufficient optimality conditions

Abstract: Summary In this paper, we derive the necessary and sufficient conditions for optimal singular control for systems governed by general controlled McKean‐Vlasov differential equations, in which the coefficients depend on the state of the solution process as well as of its law and control. The control domain is assumed to be convex. The control variable has 2 components, ie, the first being absolutely continuous and the second being singular. The proof of our result is based on the derivative of the solution proc… Show more

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Cited by 13 publications
(19 citation statements)
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“…Optimal control problems for McKean‐Vlasov‐type stochastic differential equations (SDEs) have been studied by many authors; see, for example, previous studies. Peng's type necessary conditions in the form of maximum principle for SDEs of mean‐field type have proved by Buckdahn et al The necessary optimality conditions for SDEs have been established by Wang et al Stochastic optimal control of mean‐field jump‐diffusion systems with delay has been studied by Meng and Shen . The necessary and sufficient conditions for mean‐field SDEs governed by Teugels martingales associated to Lévy process have been studied in previous studies .…”
Section: Introductionmentioning
confidence: 99%
“…Optimal control problems for McKean‐Vlasov‐type stochastic differential equations (SDEs) have been studied by many authors; see, for example, previous studies. Peng's type necessary conditions in the form of maximum principle for SDEs of mean‐field type have proved by Buckdahn et al The necessary optimality conditions for SDEs have been established by Wang et al Stochastic optimal control of mean‐field jump‐diffusion systems with delay has been studied by Meng and Shen . The necessary and sufficient conditions for mean‐field SDEs governed by Teugels martingales associated to Lévy process have been studied in previous studies .…”
Section: Introductionmentioning
confidence: 99%
“…The history of mean‐field–type SDEs, also known as McKean‐Vlasov systems, can be traced back to the works by Kac in 1956 and McKean in 1966 on stochastic systems with a large number of interacting particles. Optimal control problems for McKean‐Vlasov–type SDEs have been studied by many authors; see, for example, other works . The partial‐information maximum principle of optimality for SDEs has been established by Wang et al Stochastic optimal control of mean‐field jump‐diffusion systems with delay has been studied by Meng and Shen .…”
Section: Introductionmentioning
confidence: 99%
“…Controlled McKean‐Vlasov–type FBSDEs have been studied by Carmona and Delarue . Singular optimal control problem for general controlled nonlinear SDEs, in which the coefficients depend on the state of the solution process as well as of its law and control, has been investigated by Hafayed et al…”
Section: Introductionmentioning
confidence: 99%
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