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

2016/06/14 by Salah Eddine Choutri, Choutri, Salah Eddine, Boualem Djehiche +4 · 1 citation
Computer Science · Economics, Econometrics and Finance · Mathematics · #Markov Chains and Monte Carlo Methods #Stochastic processes and financial applications #Stochastic processes and statistical mechanics #cs.GT #math.OC #math.PR

paper · pdf · doi:10.48550/arxiv.1606.04244

arXiv admin note: text overlap with arXiv:1603.06071

arxiv created 2017/08/27 · arxiv updated 2017/08/29

Abstract

We establish existence of Markov chains of mean-field type with unbounded jump intensities by means of a fixed point argument using the Total Variation distance. We further show existence of nearly-optimal controls and, using a Markov chain backward SDE approach, we 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 payoff functionals of mean-field type, under dynamics driven by such Markov chains of mean-field type.

Citations

• Optimal control and zero-sum stochastic differential game problems of mean-field type

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