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Open AccessArticle

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

Choutri, S.E.; Hamidou, T. A Stochastic Maximum Principle for Markov Chains of Mean-Field Type. Games 2018, 9, 84.

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