Mean-field risk sensitive control and zero-sum games for Markov chains

2018/01/23 by Salah Eddine Choutri, Choutri, Salah Eddine, Boualem Djehiche +1 · 1 citation
Mathematics · #49N90 #60H07 #60H10 #FOS: Mathematics #Optimization and Control (math.OC) #Probability (math.PR) #math.OC #math.PR #msc:49N90 #msc:60H07 #msc:60H10

paper · pdf · doi:10.48550/arxiv.1801.08413

arXiv admin note: text overlap with arXiv:1606.04244

arxiv created 2018/01/23 · arxiv updated 2018/01/26

Abstract

We establish existence of controlled Markov chain of mean-field type with unbounded jump intensities by means of a fixed point argument using the Wasserstein distance. Using a Markov chain entropic backward SDE approach, we further suggest conditions for existence of an optimal control and a saddle-point for respectively a control problem and a zero-sum differential game associated with risk sensitive payoff functionals of mean-field type.

Citations

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

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