This book presents an overview of the risks involved in modern electricity production, delivery and trading, including technical risk in production, transportation and delivery, operational risk for the system operators, market risks for traders, and political and other long term risks in strategic management. Using decision making under uncertainty as a methodological background, the book is divided into four parts, with Part I focusing on energy markets, particularly electricity markets. Topics include a nontechnical overview of energy markets and their main properties, basic price models for energy commodity prices, and modeling approaches for electricity price processes. Part II looks at optimal decisions in managing energy systems, including hydropower dispatch models, cutting plane algorithms and approximative dynamic programming; hydro-thermal production; renewable; stochastic investments and operational optimization models for natural gas transport; decision making in operating electricity networks; and investment in extending energy production systems. Part III explores pricing, including electricity swing options and the pricing of derivatives with volume control. Part IV looks at long-term and political risks, including energy systems under aspects of climate change, and catastrophic operational risks, particularly risks from terrorist attacks.

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.

This book presents an overview of the risks involved in modern electricity production, delivery and trading, including technical risk in production, transportation and delivery, operational risk for the system operators, market risks for traders, and political and other long term risks in strategic management.Using decision making under uncertainty as a methodological background, the book is divided into four parts, with Part I focusing on energy markets, particularly electricity markets.Topics include a nontechnical overview of energy markets and their main properties, basic price models for energy commodity prices, and modeling approaches for electricity price processes.

Part II looks at optimal decisions in managing energy systems, including hydropower dispatch models, cutting plane algorithms and approximative dynamic programming; hydro-thermal production; renewable; stochastic investments and operational optimization models for natural gas transport; decision making in operating electricity networks; and investment in extending energy production systems.

Part III explores pricing, including electricity swing options and the pricing of derivatives with volume control. Part IV looks at long-term and political risks, including energy systems under aspects of climate change, and catastrophic operational risks, particularly risks from terrorist attacks."

The interaction of various ideas from different researchers provides a main impetus to mathematical prosress. An important way to make communication possible is through international conferences on more or less spezialized topics~ The existence of several centers for research in probabil ity and statistics in the eastern part of central Europe - somewhat vaguely described as the Pannonian area - led to the idea of organizing Pannonian Symposia on Mathematical Statistics (PS~1S). The second such symposium was held at Bad Tatzmannsdorf, Burgenland (Austria), from 14 to 20 June 1981. About 100 researchers from 13 countries participated in that event and about 70 papers were delivered. Most of the papers dealt with one of the following topics: nonparametric estimation theory, asymptotic theory of estimation, invariance principles, limit theorems and aoplications. Full versions of selected papers, all presenting new results are included in this volume. The editors take this opportunity to thank the following institutions for their assistance in making the conference possible: the Provincial Government of Burgenland, the Austrian Ministry for Research and Science, the Burgenland Chamber of Commerce, the Control Data Corporation, the Austrian Society for Statistics and Informatics, the Landes- hypothekenbank Burgenland, the Volksbank Oberwart, and the Community and Kurbad AG of Bad Tatzmannsdorf. We are also greatly indebted to all those persons who helped in editing this volume and in particular to the vii W. Grossmann et al. reds.), Probability and Statistical Inference, vii-viii.

Uncertainties and changes are pervasive characteristics of modern systems involving interactions between humans, economics, nature and technology. These systems are often too complex to allow for precise evaluations and, as a result, the lack of proper management (control) may create significant risks. In order to develop robust strategies we need approaches which explic itly deal with uncertainties, risks and changing conditions. One rather general approach is to characterize (explicitly or implicitly) uncertainties by objec tive or subjective probabilities (measures of confidence or belief). This leads us to stochastic optimization problems which can rarely be solved by using the standard deterministic optimization and optimal control methods. In the stochastic optimization the accent is on problems with a large number of deci sion and random variables, and consequently the focus ofattention is directed to efficient solution procedures rather than to (analytical) closed-form solu tions. Objective and constraint functions of dynamic stochastic optimization problems have the form of multidimensional integrals of rather involved in that may have a nonsmooth and even discontinuous character - the tegrands typical situation for "hit-or-miss" type of decision making problems involving irreversibility ofdecisions or/and abrupt changes ofthe system. In general, the exact evaluation of such functions (as is assumed in the standard optimization and control theory) is practically impossible. Also, the problem does not often possess the separability properties that allow to derive the standard in control theory recursive (Bellman) equations."

Stochastic models are everywhere. In manufacturing, queuing models are used for modeling production processes, realistic inventory models are stochastic in nature. Stochastic models are considered in transportation and communication. Marketing models use stochastic descriptions of the demands and buyer's behaviors. In finance, market prices and exchange rates are assumed to be certain stochastic processes, and insurance claims appear at random times with random amounts. To each decision problem, a cost function is associated. Costs may be direct or indirect, like loss of time, quality deterioration, loss in production or dissatisfaction of customers. In decision making under uncertainty, the goal is to minimize the expected costs. However, in practically all realistic models, the calculation of the expected costs is impossible due to the model complexity. Simulation is the only practicable way of getting insight into such models. Thus, the problem of optimal decisions can be seen as getting simulation and optimization effectively combined. The field is quite new and yet the number of publications is enormous. This book does not even try to touch all work done in this area. Instead, many concepts are presented and treated with mathematical rigor and necessary conditions for the correctness of various approaches are stated. Optimization of Stochastic Models: The Interface Between Simulation and Optimization is suitable as a text for a graduate level course on Stochastic Models or as a secondary text for a graduate level course in Operations Research.

The interaction of various ideas from different researchers provides a main impetus to mathematical prosress. An important way to make communication possible is through international conferences on more or less spezialized topics~ The existence of several centers for research in probabil ity and statistics in the eastern part of central Europe - somewhat vaguely described as the Pannonian area - led to the idea of organizing Pannonian Symposia on Mathematical Statistics (PS~1S). The second such symposium was held at Bad Tatzmannsdorf, Burgenland (Austria), from 14 to 20 June 1981. About 100 researchers from 13 countries participated in that event and about 70 papers were delivered. Most of the papers dealt with one of the following topics: nonparametric estimation theory, asymptotic theory of estimation, invariance principles, limit theorems and aoplications. Full versions of selected papers, all presenting new results are included in this volume. The editors take this opportunity to thank the following institutions for their assistance in making the conference possible: the Provincial Government of Burgenland, the Austrian Ministry for Research and Science, the Burgenland Chamber of Commerce, the Control Data Corporation, the Austrian Society for Statistics and Informatics, the Landes- hypothekenbank Burgenland, the Volksbank Oberwart, and the Community and Kurbad AG of Bad Tatzmannsdorf. We are also greatly indebted to all those persons who helped in editing this volume and in particular to the vii W. Grossmann et al. reds.), Probability and Statistical Inference, vii-viii.

Dieses Buch ist aus mehreren Vorlesungen hervorgegangen, die ich an den Universitaten GieBen und Wien gehalten habe. Die Titel dieser Vorlesungen waren: "Warteschlangentheorie," "Simulation," "Mustererkennung" und "OR-Probleme bei der Erstellung von Betriebssystemen." Allen diesen Vorlesungen war gemeinsam, daB sie Teilaspekte der Wahrscheinlichkeitstheorie unter dem Gesichtspunkt der Anwendung im weiten Gebiet der Informatik zum Inhalt hatten. Es ist nicht die Intention dieses Buches, die Lekture von Literatur uber die Technik von Betriebssystemrealisierungen oder uber spezielle Must- erkennungsverfahren uberflussig zu machen. Vielmehr soli, erganzend zur "technischen" Literatur hier gezeigt werden, wie durch die wahrscheinlichkeits theoretische Modellbildung Begriffe wie "effizient," "optimal" oder "mittlere Performance" erst ihre Bedeutung bekommen. Dabei wird auf die mathematische Korrektheit der Argumentation ebensoviel Wert gelegt, wie auf die leichtverstandliche Darstellung. Ein groBer Teil der InformatikliteratlU enthalt Resultate zur Performance, die mit Mitteln der Wahrscheinlichkeitsrechnung gefundeh wurden. Meiner Erfahrung nach fehlt jedoch einigen Informatikstudenten das Rustzeug, diese Resultate auch wirklich nachvollziehen zu konnen, so daB oft diese Teile der Arbeiten uberlesen werden. AuBerdem finden sich manchmal auch in Originalarbeiten fehlerhafte Argumentationen, wenn mit Begriffen aus der Wahrscheinlichkeitstheorie umgegangen wird. Dieses Buch soli den Einstieg in die Methodik stochastischer Modellbildung in der Informatik erleichtern."

This book is the first in the market to treat single- and multi-period risk measures (risk functionals) in a thorough, comprehensive manner. It combines the treatment of properties of the risk measures with the related aspects of decision making under risk.The book introduces the theory of risk measures in a mathematically sound way. It contains properties, characterizations and representations of risk functionals for single-period and multi-period activities, and also shows the embedding of such functionals in decision models and the properties of these models.