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

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.

arXiv admin note: text overlap with arXiv:1603.06071

References in corpus (1)

• Backward stochastic differential equation driven by a marked point process: An elementary approach with an application to optimal control

Cited by in corpus (1)

• A Stochastic Maximum Principle for Markov chains of mean-field type