Numerical analysis of stochastic control problems.

Summary The purpose of this thesis is to study the numerical approximations of different HJB equations associated with stochastic optimal control problems. In the first part, the theory of error estimation has been extended to a differential game problem and to the case of the problem with impulses. The latter has been numerically implemented. In all this part the control set is bounded. Then, in the second part of the thesis, we studied stochastic control problems coming from finance and whose set of controls is not bounded, in particular problems of over-coverage.