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Games 2018, 9(4), 84; https://doi.org/10.3390/g9040084

A Stochastic Maximum Principle for Markov Chains of Mean-Field Type

1
Department of Mathematics, KTH Royal Institute of Technology, 100 44 Stockholm, Sweden
2
Learning and Game Theory Laboratory, New York University Abu Dhabi, P.O. Box 129188, Abu Dhabi, UAE
*
Author to whom correspondence should be addressed.
Received: 4 September 2018 / Revised: 16 October 2018 / Accepted: 17 October 2018 / Published: 21 October 2018
(This article belongs to the Special Issue Mean-Field-Type Game Theory)
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Abstract

We derive sufficient and necessary optimality conditions in terms of a stochastic maximum principle (SMP) for controls associated with cost functionals of mean-field type, under dynamics driven by a class of Markov chains of mean-field type which are pure jump processes obtained as solutions of a well-posed martingale problem. As an illustration, we apply the result to generic examples of control problems as well as some applications. View Full-Text
Keywords: mean-field; nonlinear Markov chain; backward SDEs; optimal control; stochastic maximum principle mean-field; nonlinear Markov chain; backward SDEs; optimal control; stochastic maximum principle
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).
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Choutri, S.E.; Hamidou, T. A Stochastic Maximum Principle for Markov Chains of Mean-Field Type. Games 2018, 9, 84.

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