This volume is devoted to the investigation of general Borel models of stochastic optimal control, taking into consideration additional performance criteria which must satisfy the constraints-inequalities. This study is based on both convex programming theory as well as the Bellman principle, and provides a useful approach for multicriteria control problems. Some new original properties of strategical measure space are established, and among the other subjects that are treated are the existence and the form of optimal control strategy; Markov and homogeneous models; and linear-quadratic systems. The last chapter concentrates on application of these methods to, for example, economics, ecology, insurance and games. Audience: This book will be of interest to post-graduate students and researchers whose work involves stochastic control and its applications.