2019
DOI: 10.1186/s13662-019-2283-1
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Maximum principle for delayed stochastic mean-field control problem with state constraint

Abstract: In this paper, we consider the optimal control problem for the mean-field stochastic differential equations with delay and state constraint. By virtue of the classical Ekeland's variational principle, the duality method and a new type of mean-field anticipated backward stochastic differential equation, we obtain the maximum principle of the optimal control for this problem. Our result can be applied to a harvest model from a mean-field system with delay.

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Cited by 7 publications
(3 citation statements)
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“…There exists some recent works dealing with mean-field control under some specific law state constraints. For example, the paper [18] solves mean-field control with delay and smooth expectation terminal constraint (and without dependence with respect to the law of the control). In the case of mean field games, state constraints are considered by [12,13,26,30,3].…”
Section: Maximilien Germain and Huy êN Pham And Xavier Warinmentioning
confidence: 99%
“…There exists some recent works dealing with mean-field control under some specific law state constraints. For example, the paper [18] solves mean-field control with delay and smooth expectation terminal constraint (and without dependence with respect to the law of the control). In the case of mean field games, state constraints are considered by [12,13,26,30,3].…”
Section: Maximilien Germain and Huy êN Pham And Xavier Warinmentioning
confidence: 99%
“…There exists some recent works dealing with mean-field control under some specific law state constraints. For example, the paper [18] solves mean-field control with delay and smooth expectation terminal constraint (and without dependence with respect to the law of the control). In the case of mean field games, state constraints are considered by [12,13,28,33,3].…”
Section: Introductionmentioning
confidence: 99%
“…Necessary conditions for optimal control with constraints for mean-field forward-backward stochastic differential equation have been studied by Wei [24]. Maximum principle for delayed stochastic mean-field control problem with state constraint has been investigated by Chen and Wang [16].…”
mentioning
confidence: 99%