This volume investigates general Borel models of stochastic optimal control, focusing on performance criteria that must satisfy inequality constraints. The study integrates convex programming theory and the Bellman principle to address multicriteria control problems. It establishes novel properties of strategical measure space and examines the existence and form of optimal control strategies, Markov and homogeneous models, and linear-quadratic systems. The final chapter applies these methods to fields such as economics, ecology, insurance, and games.

This book is aimed at post-graduate students and researchers working in stochastic control and its applications. The text is expected to provide a rigorous theoretical framework for complex control problems, drawing on established mathematical principles. Its interdisciplinary approach suggests utility for those applying mathematical modeling to economic, ecological, or game-theoretic scenarios. The detailed examination of specific models and systems indicates a focus on advanced theoretical and applied research.