Martin Beckmann is going to celebrate his sixtieth birthday. This is almost unbelievable considering the vitality, ingenuity, and activity which he continues to show as he always did. It is an honor able and pleasant duty for the whole economics community to show hirn the respect, gratitude, and affection which he deserves. Thus, those' who have contributed to this festschrift may be thought of as a dele gation from a much larger community in which all of us are joined; the editors in particular feel deeply connected with and enriched by the personality and scientific work of Martin Beckmann. Martin Beckmann is one of those rare scholars who are not narrow minded specialists in one field; he has been active in many areas of economics and operations research which rapidly developed since World War 11, and he has contributed original and fruitful ideas in almost all of them. The variety of topics treated in this volume aims to re flect the impressive width of his scientific interests."

The lift zonoid approach is based on a new representation of probability measures: a d-variate probability measure is represented by a convex set, its lift zonoid. First, lift zonoids are useful in data analysis to describe an empiricaldistribution by central (so-called trimmed) regions. They give rise to a concept of data depth related to the mean which is also useful in nonparametric tests for location and scale. Second, for comparing random vectors, the set inclusion of lift zonoids defines a stochastic order that reflects the dispersion of random vectors. This has many applications to stochastic comparison problems in economics and other fields. This monograph ves the first account in book form of the theory of lift zonoids and demonstrates its usefulness in multivariate analysis. Chapter 1 offers the reader an informal introduction to basic ideas, Chapter 2 presents a comprehensive investigation into the theory. The remaining seven chapters treat various applications of the lift zonoid approach and may be separately studied. Readers are assumed to have a firm grounding in probability at the graduate level. Karl Mosler is Professor of Statistics and Econometrics at the University of Cologne. He is Editor of the Allgemeines Statistisches Archive, Journal of the German Statistical Society, and has authored numerous research articles and four books (all with Springer-Verlag) in statistics and operations research.

A bibliography on stochastic orderings. Was there a real need for it? In a time of reference databases as the MathSci or the Science Citation Index or the Social Science Citation Index the answer seems to be negative. The reason we think that this bibliog raphy might be of some use stems from the frustration that we, as workers in the field, have often experienced by finding similar results being discovered and proved over and over in different journals of different disciplines with different levels of mathematical so phistication and accuracy and most of the times without cross references. Of course it would be very unfair to blame an economist, say, for not knowing a result in mathematical physics, or vice versa, especially when the problems and the languages are so far apart that it is often difficult to recognize the analogies even after further scrutiny. We hope that collecting the references on this topic, regardless of the area of application, will be of some help, at least to pinpoint the problem. We use the term stochastic ordering in a broad sense to denote any ordering relation on a space of probability measures. Questions that can be related to the idea of stochastic orderings are as old as probability itself. Think for instance of the problem of comparing two gambles in order to decide which one is more favorable."

The 17th Symposium on Operations Research was held at UniversitAt der Bundeswehr Hamburg, August 25-28, 1992, as the annual meeting of the Gesellschaft fA1/4r Mathematik, A-konomie und Operations Research (GMA-OR). The aim of this book is to provide a timely and comprehensive documentation of the symposium's scientific activities. It contains extended abstracts of most of the papers presented there. The symposium fell into twelve sections and an overlapping cross-section workshop. The sections covered established fields of theory and application such as (1) Mathematical Modelling in OR, (2) Stochastic Models of OR, (3) Combinatorial Optimization and Discrete Mathematics, (4) Linear and Non-Linear Optimization, (5) Systems and Control Theory, (6) Decision Support and Information Systems, (7) Applications in Business and Economics, (8) Econometrics and Statistics, (9) Micro-Economics and Game Theory, Macro-Economics and Applied Economics, Decision Theory, Utility and Risk, Banking, Finance and Insurance. As a novelty and an experiment, a cross-section workshop on Environmental Systems and Economics had been included in the program which was devoted to a topic of current political and scientific interest.

Das Buch bietet eine Einfuhrung in die wichtigsten Methoden der Wahrscheinlichkeitsrechnung und des statistischen Schliessens, das heisst, der Schatzung von Parametern und des Testens von Hypothesen. Die Autoren bemuhen sich um klare Begrifflichkeiten, nachvollziehbare Verfahren und Motivation aus den Wirtschaftswissenschaften. Der Band enthalt zahlreiche durchgerechnete Beispiele sowie Hinweise zur Anwendung mit Excel (R) und SPSS (R). Das Lehrbuch richtet sich insbesondere an Studierende der Wirtschafts- und Sozialwissenschaften im Grundstudium.

Das Buch bietet eine Einfuhrung in die wichtigsten Methoden der beschreibenden Statistik und ausgewahlte Kapitel der Wirtschaftsstatistik, insbesondere in die Indexzahlen und die Messung von Konzentration und Disparitat. Die Darstellung zielt auf klare Begriffe, nachvollziehbare Verfahren und Motivation aus den Wirtschaftswissenschaften. Sie enthalt zahlreiche durchgerechnete Beispiele, zum Teil mit aktuellen realen Wirtschaftsdaten. Anleitungen zur Datenanalyse am Computer mit Excel(r) erganzen den Text. Das Lehrbuch richtet sich an Studierende insbesondere der Wirtschafts- und Sozialwissenschaften im Bachelorstudium. Es ist auch zum Selbststudium geeignet."

Das Buch bietet eine Einfuhrung in die wichtigsten mathematischen Methoden fur OEkonomen. Dazu gehoeren das Optimieren von Funktionen mit und ohne Nebenbedingungen, das Loesen linearer Gleichungssysteme, die Analyse von Differential- und Differenzengleichungen sowie die lineare Optimierung. Die Autoren legen besonderen Wert auf die Darstellung relevanter wirtschaftswissenschaftlicher Begriffe und Modelle. Eine ubersichtliche Darstellung, zahlreiche Abbildungen sowie durchgerechnete Beispiele und Aufgaben mit Kurzloesungen erleichtern das Selbststudium.