Overview
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 RiskMeasuresinTwo-StageStochasticPrograms 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 StochasticDominanceConstraints 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 dominanceconstraints. . . . . . . . 43 3. 2. 2 Results concerning structure and stability . . . . . . . . . 44 3. 2. 3 Deterministic equivalents. . . . . . . . . . . . . . . . . . 51 3. 2. 4 Algorithmic issues . . . . . . . . . . . . . . . . . . . . .
Full Product Details
Author: Frederike Neise
Publisher: Springer Fachmedien Wiesbaden
Imprint: Vieweg+Teubner Verlag
Edition: 2008 ed.
Dimensions:
Width: 14.80cm
, Height: 0.60cm
, Length: 21.00cm
Weight: 0.454kg
ISBN: 9783834805478
ISBN 10: 3834805475
Pages: 107
Publication Date: 28 July 2008
Audience:
Professional and scholarly
,
Professional & Vocational
Format: Paperback
Publisher's Status: Active
Availability: In Print
This item will be ordered in for you from one of our suppliers. Upon receipt, we will promptly dispatch it out to you. For in store availability, please contact us.
Language: English
Author Information
Dr. Frederike Neise gained a PhD in Mathematics from the University of Duisburg-Essen studying two-stage stochastic programming and its application to the optimal management of dispersed generation systems. She currently works as a gas market analyst with E.ON Ruhrgas AG.
