Mean-Field Optimal Control of Di¤usion with Regime Switching

Abstract

The objective of this thesis is to study a problem of optimal control with regime switching jump-di¤usion model of mean-…eld type. In the …rst part we recall a result in the stochastic maximum principle whose horizon is …nite. In the second part, we devote ourselves to presenting the two main results of this thesis, in the …rst result we give the necessary and su¢ cient conditions of optimality whose control system is governed by a stochastic di¤erential equation with regime switching of in…nite horizon and by way of illustration, we have given two examples where in both cases the equation of state is linear and the objective function is of utility form. The second contribution on the maximum principle for a control problem of conditional mean …eld type of …nite horizon, we illustrate our result by a model which gives an explicit solution