Risk management in stochastic integer programming : with application to dispersed power generation / Frederike Neise.
"I am deeply grateful to my advisor Prof. Dr. Rüdiger Schultz for his untiring - couragement. Moreover, I would like to express my gratitude to Prof. Dr. -Ing. - mund Handschin and Dr. -Ing. Hendrik Neumann from the University of Dortmund for inspiration and support. I would like to thank PD Dr...
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| Main Author: | |
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| Format: | Ebook |
| Language: | English |
| Published: |
Wiesbaden :
Vieweg + Teubner,
2008.
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| Edition: | 1. edition. |
| Series: | Vieweg+Teubner research.
Wissenschaft (Vieweg+Teubner). |
| Subjects: | |
| Online Access: | Springer eBooks |
| Summary: | "I am deeply grateful to my advisor Prof. Dr. Rüdiger Schultz for his untiring - couragement. Moreover, I would like to express my gratitude to Prof. Dr. -Ing. - mund Handschin and Dr. -Ing. Hendrik Neumann from the University of Dortmund for inspiration and support. I would like to thank PD Dr. René Henrion from the Weierstrass Institute for Applied Analysis and Stochastics in Berlin for reviewing this thesis. Cordial thanks to my colleagues at the University of Duisburg-Essen for motivating and fruitful discussions as well as a pleasurable cooperation. Contents 1 Introduction 1 1. 1 Stochastic Optimization. . . . . . . . . . . . . . . . . . . . . . . 3 1. 1. 1 The two-stage stochastic optimization problem . . . . . . 3 1. 1. 2 Expectation-based formulation. . . . . . . . . . . . . . . 5 1. 2 Content and Structure. . . . . . . . . . . . . . . . . . . . . . . . 6 2 Risk Measuresin Two-Stage Stochastic Programs 9 2. 1 Risk Measures. . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 2. 1. 1 Deviation measures. . . . . . . . . . . . . . . . . . . . . 10 2. 1. 2 Quantile-based risk measures . . . . . . . . . . . . . . . 11 2. 2 Mean-Risk Models . . . . . . . . . . . . . . . . . . . . . . . . . 12 2. 2. 1 Results concerning structure and stability . . . . . . . . . 13 2. 2. 2 Deterministic equivalents. . . . . . . . . . . . . . . . . . 22 2. 2. 3 Algorithmic issues – dual decomposition method . . . . . 26 3 Stochastic Dominance Constraints 33 3. 1 Introduction to Stochastic Dominance . . . . . . . . . . . . . . . 33 3. 1. 1 Stochastic orders for the preference of higher outcomes . . 34 3. 1. 2 Stochastic orders for the preference of smaller outcomes . 38 3. 2 Stochastic Dominance Constraints . . . . . . . . . . . . . . . . . 42 3. 2. 1 First order stochastic dominance constraints. . . . . . . . 43 3. 2. 2 Results concerning structure and stability . . . . . . . . . 44 3. 2. 3 Deterministic equivalents. . . . . . . . . . . . . . . . . . 51 3. 2. 4 Algorithmic issues . . . . . . . . . . . . . . . . . . . . ."--Publisher's website. |
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| Physical Description: | 1 online resource (viii, 105 pages) : illustrations. |
| Format: | Mode of access: World Wide Web. |
| Bibliography: | Includes bibliographical references. |
| ISBN: | 1281795208 3834895369 9781281795205 9783834895363 |