Contributions to the Stochastic Maximum Principle

摘要

This thesis consists of four papers treating the maximum principle for stochastic control problems. In the first paper we study the optimal control of a class of stochastic differential equations (SDEs) of mean-field type, where the coefficients are allowed to depend on the law of the process. In the second paper, we study the problem of controlling a linear SDE where the coefficients are random and not necessarily bounded. The third paper generalizes the second one by adding a singular control process to the SDE. In the fourth paper we consider a general singular control.