Multistage stochastic optimization problems appear in many ways in finance, insurance, energy production and trading, logistics and transportation, among other areas. They describe decision situations under uncertainty and with a longer planning horizon. This book contains a comprehensive treatment of today's state of the art in multistage stochastic optimization. It covers the mathematical backgrounds of approximation theory as well as numerous practical algorithms and examples for the generation and handling of scenario trees. A special emphasis is put on estimation and bounding of the modeling error using novel distance concepts, on time consistency and the role of model ambiguity in the decision process. An extensive treatment of examples from electricity production, asset liability management and inventory control concludes the book.
Georg Pflug is full professor of Statistics and Operations Research at the University of Vienna, Austria. He got a PhD in Mathematics from the University of Vienna and was Professor of Mathematics at the University of Giessen, Germany, before joining the University of Vienna as a full professor. He is author of 4 books and more than 80 peer reviewed articles. He is also editor of several books and special issues of journals.
Alois Pichler holds a PhD in economic sciences and master degrees in mathematics and physics. He has gathered business experience in different positions in the insurance and banking industry, including managerial positions. He is with the Norwegian University of Science and Technology and his scientific work is dedicated to mathematical properties of risk measures with a particular focus on their relation to insurance, and to optimization under uncertainty.
Introduction.- The Nested Distance.- Risk and Utility Functionals.- From Data to Models.- Time Consistency.- Approximations and Bounds.- The Problem of Ambiguity in Stochastic Optimization.- Examples.