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This book studies a general class of convex stochastic optimization (CSO) problems that unifies many common problem formulations from operations research, financial mathematics and stochastic optimal control. We extend the theory of dynamic programming and convex duality to allow for a unified and simplified treatment of various special problem classes found in the literature. The extensions allow also for significant generalizations to existing problem formulations. Both dynamic programming and duality have played crucial roles in the development of various optimality conditions and numerical techniques for the solution of convex stochastic optimization problems.
Inhaltsverzeichnis
- 1. Convex Stochastic Optimization. - 2. Dynamic Programming. - 3. Duality. - 4. Absence of a Duality Gap. - 5. Existence of Dual Solutions.
The book integrates classical models with significant new generalizations, covering discrete-time stochastic control, financial mathematics, and inequality-constrained stochastic programs. Each chapter includes both theoretical foundations and applied results. Appendices review key tools from convex analysis and probability. The book provides a modern approach to convex stochastic optimization that unifies and extends existing theory. For that reason this book will be a valuable reading for researchers and advanced students in stochastic optimization, mathematical finance, operations research, and stochastic optimal control. (Marcin Anholcer, Mathematical Reviews, February, 2026)
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