Risk management in stochastic integer programming

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I extend my heartfelt gratitude to my advisor, Prof. Dr. Rüdiger Schultz, for his unwavering encouragement. I also appreciate the inspiration and support from Prof. Dr. -Ing. -mund Handschin and Dr. -Ing. Hendrik Neumann at the University of Dortmund. Special thanks to PD Dr. René Henrion from the Weierstrass Institute for Applied Analysis and Stochastics in Berlin for reviewing this thesis. I am grateful to my colleagues at the University of Duisburg-Essen for their motivating discussions and enjoyable collaboration. The work begins with an introduction to stochastic optimization, detailing the two-stage stochastic optimization problem and its expectation-based formulation. The subsequent sections delve into risk measures in two-stage stochastic programs, covering deviation measures and quantile-based risk measures, along with mean-risk models, their structure, stability, deterministic equivalents, and algorithmic issues such as the dual decomposition method. The discussion progresses to stochastic dominance constraints, introducing stochastic orders for preferences of higher and lower outcomes. It examines first-order stochastic dominance constraints, their structural and stability results, deterministic equivalents, and relevant algorithmic challenges. This comprehensive exploration aims to enhance understanding and application of stochastic optimization and its associated concepts.