Table of Contents

1 Methods of Stochastic Optimal Control.- 1.1 Statement of the optimal control problem and examples.- 1.2 Markov decision processes.- 2 Optimal Control Problems with Constraints.- 2.1 Statement of the problem.- 2.2 Properties of the strategic measures space.- 2.3 Necessary and sufficient conditions for optimality.- 2.4 Essential and inessential constraints.- 2.5 Algorithm for solving the main convex programming problem.- 2.6 Example.- 3 Solvability of the main constrained problem and some extensions.- 3.1 Existence of solutions in constrained problems.- 3.2 Form of optimal control strategies.- 3.3 Example.- 3.4 Other constrained problems of optimal control.- 4 Linear-quadratic systems.- 4.1 Model with a finite horizon.- 4.2 Homogeneous discounted model.- 4.3 Homogeneous model with average losses.- 5 Some applications.- 5.1 Stochastic macroeconomic model of the Neumann type.- 5.2 Simplest ecological-economic system.- 5.3 Model of insurance.- 5.4 Stochastic stabilization problem.- 5.5 Queueing system.- 5.6 Optimization of publicity expenses.- 5.7 Simplest constrained game.- Conclusion.- A1 Borel spaces and their properties.- A1.1 Main concepts.- A1.2 Probability measures on Borel spaces.- A1.3 Semicontinuous functions and measurable selection.- A2 Elements of convex analysis.- A2.1 Certain definitions.- A2.2 Duality relation and Kuhn-Tucker theorem.- A2.3 Selected properties of convex sets.- A3 Proofs of auxiliary statements.- A4 Linear-quadratic systems: proofs of some statements.- References.- List of symbols.- List of the main statements.

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