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Mean-field backward-forward stochastic differential equations and nonzero sum stochastic differential gamesApr 12 2019We study a general class of fully coupled backward-forward stochastic differential equations of mean-field type (MF-BFSDE). We derive existence and uniqueness results for such a system under weak monotonicity assumptions and without the non-degeneracy ... More
Stability of Mc Kean-Vlasov stochastic differential equations and applicationsFeb 09 2019We consider Mc Kean-Vlasov stochastic differential equations (MVSDEs), which are SDEs where the drift and diffusion coefficients depend not only on the state of the unknown process but also on its probability distribution. This type of SDEs was studied ... More
A Stochastic Maximum Principle for Markov chains of mean-field typeSep 06 2018We 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 ... More
Mean-field risk sensitive control and zero-sum games for Markov chainsJan 23 2018We 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 ... More
On relaxed stochastic optimal control for stochastic differential equations driven by G-Brownian motionFeb 28 2017In the G-framework, we establish existence of an optimal stochastic relaxed control for stochastic differential equations driven by a G-Brownian motion.
Optimal control and zero-sum stochastic differential game problems of mean-field typeMar 19 2016We show existence of an optimal control and a saddle-point for respectively a control problem and zero-sum differential game associated with payoff functionals of mean field type, under dynamics driven by weak solutions of stochastic differential equations ... More
Optimal control and zero-sum stochastic differential game problems of mean-field typeMar 19 2016Nov 30 2016We show existence of an optimal control and a saddle-point for respectively a control problem and zero-sum differential game associated with payoff functionals of mean field type, under dynamics driven by weak solutions of stochastic differential equations ... More
Optimal control and zero-sum stochastic differential game problems of mean-field typeMar 19 2016Jul 22 2017We establish existence of nearly-optimal controls, conditions for existence of an optimal control and a saddle-point for respectively a control problem and zero-sum differential game associated with payoff functionals of mean-field type, under dynamics ... More