Infinite horizon optimal control of mean-field delay system with semi-Markov modulated jump-diffusion processes

Deepa, R.; Muthukumar, P.

doi:10.1007/s41478-018-0098-1

Cited by 7 publications

(3 citation statements)

References 27 publications

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“…Linear quadratic optimal control problem for conditional mean-field equation with random coefficients with applications has been investigated by Pham [19]. Infinite horizon optimal control problems for mean-field delay system with semi-Markov modulated jump-diffusion processes have been investigated by Deepa and Muthukumar [20]. First-order necessary conditions for optimal singular control problem for general mean-field SDEs under convexity assumptions have been investigated by Hafayed et al [21].…”

Section: Introductionmentioning

confidence: 99%

On pointwise second‐order maximum principle for optimal stochastic controls of general mean‐field type

Boukaf,

Korichi,

Hafayed

et al. 2023

Asian Journal of Control

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In this paper, we establish a second‐order stochastic maximum principle for optimal stochastic control of stochastic differential equations of general mean‐field type. The coefficients of the system are nonlinear and depend on the state process as well as of its probability law. The control variable is allowed to enter into both drift and diffusion terms. We establish a set of second‐order necessary conditions for the optimal control in integral form. The control domain is assumed to be convex. The proof of our main result is based on the first‐ and second‐order derivatives with respect to the probability law and by using a convex perturbation with some appropriate estimates.

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Section: Introductionmentioning

confidence: 99%

On pointwise second‐order maximum principle for optimal stochastic controls of general mean‐field type

Boukaf,

Korichi,

Hafayed

et al. 2023

Asian Journal of Control

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“…Based on the motivation of the above literature, the authors find that the few of the works focused on optimal control of infinite‐horizon mean‐field stochastic differential games (see References 20‐23 and references therein). Infinite‐horizon optimal control problems arise naturally in economics when dealing with dynamical models of optimal allocation of resources.…”

Section: Introductionmentioning

confidence: 99%

Optimal control of nonzero sum game mean‐field delayed Markov regime‐switching forward‐backward system with Lévy processes

Deepa¹,

Muthukumar

Hafayed

2020

Optim Control Appl Methods

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SummaryThis article investigates the optimal control problem of nonzero sum game mean‐field delayed Markov regime‐switching forward‐backward stochastic system with Lévy processes associated with Teugels martingales over the infinite time horizon. Based on the transversality conditions, assumption of convex control domain, infinite‐horizon version of stochastic maximum principle (Nash equilibrium), and necessary condition for optimality are established. Finally, the Nash equilibrium for the optimization problem in the financial market is considered to illustrate the observed theoretical results.

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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%

On optimal solutions of general continuous‐singular stochastic control problem of McKean‐Vlasov type

Guenane

Hafayed

Meherrem

et al. 2020

Math Methods in App Sciences

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In this paper, we establish general necessary optimality conditions for stochastic continuous‐singular control of McKean‐Vlasov type equations. The coefficients of the state equation depend on the state of the solution process as well as of its probability law and the control variable. The coefficients of the system are nonlinear and depend explicitly on the absolutely continuous component of the control. The control domain under consideration is not assumed to be convex. The proof of our main result is based on the first‐ and second‐order derivatives, with respect to measure in Wasserstein space of probability measures, and by using variational method.

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Infinite horizon optimal control of mean-field delay system with semi-Markov modulated jump-diffusion processes

Cited by 7 publications

References 27 publications

On pointwise second‐order maximum principle for optimal stochastic controls of general mean‐field type

On pointwise second‐order maximum principle for optimal stochastic controls of general mean‐field type

Optimal control of nonzero sum game mean‐field delayed Markov regime‐switching forward‐backward system with Lévy processes

On optimal solutions of general continuous‐singular stochastic control problem of McKean‐Vlasov type

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