scholarly journals Optimal control and zero-sum games for Markov chains of mean-field type

2019 ◽  
Vol 9 (3) ◽  
pp. 571-605
Author(s):  
Salah Eddine Choutri ◽  
◽  
Boualem Djehiche ◽  
Hamidou Tembine ◽  
Keyword(s):  
Optimal Control ◽  
Markov Chains ◽  
Mean Field ◽  
Field Type ◽  
Zero Sum Games ◽  
Zero Sum

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

Games ◽  
2018 ◽  
Vol 9 (4) ◽  
pp. 84 ◽  
Author(s):  
Salah Choutri ◽  
Tembine Hamidou
Keyword(s):  
Maximum Principle ◽  
Markov Chains ◽  
Martingale Problem ◽  
Mean Field ◽  
Necessary Optimality Conditions ◽  
Stochastic Maximum Principle ◽  
Jump Processes ◽  
Field Type ◽  
Cost Functionals ◽  
Well Posed

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.

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