A stochastic maximum principle for Markov chains of mean-field type - Salah Eddine Choutri; Tembine Hamidou (Games, 2018)
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.
Keywords: 330; mean-field; nonlinear Markov chain; backward SDEs; optimal control; stochastic maximum principle