This study is a revised version of my doctoral dissertation at the Economics Department of the University of Munich. I want to take the opportunity to express my gratitude to some people who have helped me in my work. My greatest thanks go to the supervisor of this dissertation, Professor Claude Billinger. Bis ideas have formed the basis of my work. Be permanently sup ported it with a host of ideas, criticism and encouragement. Furthermore, he provided a stimulating research environment at SEMECON. This study would not have been possible in this form without the help of my present and former colleagues at SEMECON. I am indebted to Rudolf Kohne-Volland, Monika Sebold-Bender and Ulrich Woitek for providing soft ware and guidance for the data analysis. Discussions with them and with Thilo Weser have helped me to take many hurdles, particularly in the early stages of the project. My sincere thanks go to them all. I had the opportunity to present a former version of my growth model at a workshop of Professor Klaus Zimmermann. I want to thank all the parti cipants for their helpful comments. I also acknowledge critical and constructive comments from an anonymous referee. Table of Contents Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 Part I. Methodology 1. Importance of Stylized Facts. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 1.1 Limitations of statistical testing. . . . . . . . . . . . . . . . . . . . . . . . . . 9 1.2 Evaluating economic models. . . . . . . . . . . . . . . . . . .. . . . 11 . . . . . . 2. Further Methodological Issues . . . . . . . . . . . . . . . . . .. . . . 13 . . . . . ."

This new and exciting book offers a fresh approach to quantitative finance and utilises novel features, including stereoscopic images which permit 3D visualisation of complex subjects without the need for additional tools. Offering an integrated approach to the subject, A First Course in Quantitative Finance introduces students to the architecture of complete financial markets before exploring the concepts and models of modern portfolio theory, derivative pricing and fixed income products in both complete and incomplete market settings. Subjects are organised throughout in a way that encourages a gradual and parallel learning process of both the economic concepts and their mathematical descriptions, framed by additional perspectives from classical utility theory, financial economics and behavioural finance. Suitable for postgraduate students studying courses in quantitative finance, financial engineering and financial econometrics as part of an economics, finance, econometric or mathematics program, this book contains all necessary theoretical and mathematical concepts and numerical methods, as well as the necessary programming code for porting algorithms onto a computer.

This book brings together a wide range of topics and perspectives in the growing field of Classification and related methods of Exploratory and Multivariate Data Analysis. It gives a broad view on the state ofthe art, useful for those in the scientific community who gather data and seek tools for analyzing and interpreting large sets of data. As it presents a wide field of applications, this book is not only of interest for data analysts, mathematicians and statisticians, but also for scientists from many areas and disciplines concerned with real data, e. g. , medicine, biology, astronomy, image analysis, pattern recognition, social sciences, psychology, marketing, etc. It contains 79 invited or selected and refereed papers presented during the Fourth Bi- ennial Conference of the International Federation of Classification Societies (IFCS'93) held in Paris. Previous conferences were held at Aachen (Germany), Charlottesville (USA) and Edinburgh (U. K. ). The conference at Paris emerged from the elose coop- eration between the eight members of the IFCS: British Classification Society (BCS), Classification Society of North America (CSNA), Gesellschaft fur Klassifikation (GfKl), J apanese Classification Society (J CS), Jugoslovenska Sekcija za Klasifikacije (JSK), Societe Francophone de Classification (SFC), Societa. Italiana di Statistica (SIS), Vereniging voor Ordinatie en Classificatie (VOC), and was organized by INRIA ("Institut National de Recherche en Informatique et en Automatique"), Rocquencourt and the "Ecole Nationale Superieure des Telecommuni- cations," Paris.

Many models in this volume can be used in solving portfolio problems, in assessing forecasts, in understanding the possible effects of shocks and disturbances.

The papers collected in this volume are contributions to T.I.Tech./K.E.S. Conference on Nonlinear and Convex Analysis in Economic Theory, which was held at Keio University, July 2-4, 1993. The conference was organized by Tokyo Institute of Technology (T. I. Tech.) and the Keio Economic Society (K. E. S.) , and supported by Nihon Keizai Shimbun Inc .. A lot of economic problems can be formulated as constrained optimiza tions and equilibrations of their solutions. Nonlinear-convex analysis has been supplying economists with indispensable mathematical machineries for these problems arising in economic theory. Conversely, mathematicians working in this discipline of analysis have been stimulated by various mathematical difficulties raised by economic the ories. Although our special emphasis was laid upon "nonlinearity" and "con vexity" in relation with economic theories, we also incorporated stochastic aspects of financial economics in our project taking account of the remark able rapid growth of this discipline during the last decade. The conference was designed to bring together those mathematicians who were seriously interested in getting new challenging stimuli from economic theories with those economists who were seeking for effective mathematical weapons for their researches. Thirty invited talks (six of them were plenary talks) given at the conf- ence were roughly classified under the following six headings : 1) Nonlinear Dynamical Systems and Business Fluctuations, . 2) Fixed Point Theory, 3) Convex Analysis and Optimization, 4) Eigenvalue of Positive Operators, 5) Stochastic Analysis and Financial Market, 6) General Equilibrium Analysis.

As large physical capital stock projects need long periods to be built, a time-to-build specification is incorporated in factor demand models. Time-to-build and adjustment costs dynamics are identified since by the first moving average dynamics, whereas by the latter autoregressive dynamics are induced. Empirical evidence for time-to-build is obtained from data from the Dutch construction industry and by the estimation result from the manufacturing industry of six OECD countries.

This book presents a review of recent developments in the theory and construction of index numbers using the stochastic approach, demonstrating the versatility of this approach in handling various index number problems within a single conceptual framework. It also contains a brief, but complete, review of the existing approaches to index numbers with illustrative numerical examples.;The stochastic approach considers the index number problem as a signal extraction problem. The strength and reliability of the signal extracted from price and quantity changes for different commodities depends on the messages received and the information content of the messages. The most important applications of the new approach are to be found in the context of measuring rate of inflation and fixed and chain base index numbers for temporal comparisons and for spatial inter-country comparisons - the latter generally require special index number formulae that result in transitive and base invariant comparisons.

1. 1 Integrating results The empirical study of macroeconomic time series is interesting. It is also difficult and not immediately rewarding. Many statistical and economic issues are involved. The main problems is that these issues are so interrelated that it does not seem sensible to address them one at a time. As soon as one sets about the making of a model of macroeconomic time series one has to choose which problems one will try to tackle oneself and which problems one will leave unresolved or to be solved by others. From a theoretic point of view it can be fruitful to concentrate oneself on only one problem. If one follows this strategy in empirical application one runs a serious risk of making a seemingly interesting model, that is just a corollary of some important mistake in the handling of other problems. Two well known examples of statistical artifacts are the finding of Kuznets "pseudo-waves" of about 20 years in economic activity (Sargent (1979, p. 248)) and the "spurious regression" of macroeconomic time series described in Granger and Newbold (1986, 6. 4). The easiest way to get away with possible mistakes is to admit they may be there in the first place, but that time constraints and unfamiliarity with the solution do not allow the researcher to do something about them. This can be a viable argument."

This textbook on the basics of option pricing is accessible to readers with limited mathematical training. It is for both professional traders and undergraduates studying the basics of finance. Assuming no prior knowledge of probability, Sheldon M. Ross offers clear, simple explanations of arbitrage, the Black-Scholes option pricing formula, and other topics such as utility functions, optimal portfolio selections, and the capital assets pricing model. Among the many new features of this third edition are new chapters on Brownian motion and geometric Brownian motion, stochastic order relations, and stochastic dynamic programming, along with expanded sets of exercises and references for all the chapters.

As a new type of technique, simplicial methods have yielded extremely important contributions toward solutions of a system of nonlinear equations. Theoretical investigations and numerical tests have shown that the performance of simplicial methods depends critically on the triangulations underlying them. This monograph describes some recent developments in triangulations and simplicial methods. It includes the D1-triangulation and its applications to simplicial methods. As a result, efficiency of simplicial methods has been improved significantly. Thus more effective simplicial methods have been developed.

A macroeconomic disequilibrium model is developed for the Federal Republic of Germany. Starting with a microeconomic model of firm's behaviour, the optimal dynamic adjustment of employment and investment is derived. The model of the firm is complemented by an explicite aggregation procedure which allows to derive macroeconomic relations. The model is estimated with macroeconomic data for the Federal Republic of Germany. An important feature is the consistent introduction of dynamic adjustment into a model of the firm. A new method is the particular approach of a delayed adjustment of employment and investment. The estimation results show significant underutilizations of labour and capital and indicate the importance of supply constraints for imports and exports. As the most prominent result, they reveal the importance of the slow adjustment of employment and investment for the macroeconomic situation in Germany and especially for the persistence of high unemployment in the eighties.

A discussion of various aspects of dynamic behavior of empirical macroeconomic, and in particular, macroeconometric models, is presented in this book. The book addresses in depth several theoretical and practical aspects concerning the modeling and analysis of long-run equilibrium behavior, adjustment dynamics and stability. Tools are developed to identify and interpret the main determinants of the dynamics of models. The tools involve, among others, error-correction mechanisms, eigenvalue analysis, feedback closure rules, graph theory, learning behavior, steady-state analysis, and stochastic simulation. Their usefulness is demonstrated by interesting applications to a number of well-known national and multi-national models.

This graduate level textbook deals with analyzing and forecasting multiple time series. It considers a wide range of multiple time series models and methods. The models include vector autoregressive, vector autoregressive moving average, cointegrated, and periodic processes as well as state space and dynamic simultaneous equations models. Least squares, maximum likelihood, and Bayesian methods are considered for estimating these models. Different procedures for model selection or specification are treated and a range of tests and criteria for evaluating the adequacy of a chosen model are introduced. The choice of point and interval forecasts is considered and impulse response analysis, dynamic multipliers as well as innovation accounting are presented as tools for structural analysis within the multiple time series context. This book is accessible to graduate students in business and economics. In addition, multiple time series courses in other fields such as statistics and engineering may be based on this book. Applied researchers involved in analyzing multiple time series may benefit from the book as it provides the background and tools for their task. It enables the reader to perform his or her analyses in a gap to the difficult technical literature on the topic.

This book reports new developments in applied econometrics. All papers originated in two international workshops that were organized in the University of Munich on July 6-7, 1989, and on January 11 - 12, 1990. Financial support for these conferences by the University of Munich and the Thyssen Foundation is gratefully acknowledged. Since then all papers were substantially revised and updated. We wish to thank all authors for their patience with the revisions and Thomas Bauer, Lucie Merkle and Gisela Loos for editorial help. The ftrst section of the book collects contributions that address new "Methodological Developments." Two of them deal with problems in microeconometrics, the other two consider multi-equation systems. Martin Kukuk and Gerd Ronning treat "Ordinal Variables in Microeconometric Models." They especially deal with the case of limited-dependent variable models where some exogenous variables are either measured on an interval scale or a nominal scale. They discuss and compare two methods to deal with the problem. In his paper on "Goodness of Fit in Qualitative Choice Models: Review and Evaluation," Klaus F. Zimmermann investigates methods to summarize the predictive quality of models that deal with discrete alternatives. For these models, a widely accepted measure for evaluation like the R2, as in the case of ordinary least squares, does not exist. The paper summarizes the literature and suggests reasonable choices for evaluation on the basis of large-scale Monte Carlo investigations.

In contemporary labor economics increasing attention is paid to the fact that unemployment is not only a stock but also a flow phenomenon. The present micro-econometric study analyses the impact of important socio-economic characteristics on unemployment duration in West Germany. Based on a search theoretic framework unemployment duration is considered as a stochastic process whose evolution is influenced by economicand demographic variables like unemployment benefits, expected wage offers, training and age. This is modeled by application of the concept of the hazard rate which denotes the conditional exit rate from unemployment over time given elapsed unemployment duration. Contrasting more traditional models a semi-parametric approachis chosen which reduces the danger of mis-specification of the stochastic duration process. This procedure also is particularly suitable for the analysis of grouped observations on unemployment duration typically generated by longitudinal data sets as the German "Socio-Economic Panel" which is utilized for this study. Besides deriving a set of empirical results on unemployment duration in West Germanymethodological issues of duration analysis are considered with particular attention paid to the impact of the sample design. Also, important outcomes from search theory and findings from other hazard rate analysesare surveyed.

The responses to questions such as 'What is the explanation for changes in the unemployment rate?' frequently involve the presentation of a mathematical relationship, a function that relates one set of variables to another set of variables. It should become apparent that as one's understanding of functions, relationships, and variables becomes richer and more detailed, one's ability to provide explanations for economic phenomena becomes stronger and more sophisticated. The author believes that a student's intuition should be involved in the study of mathematical techniques in economics and that this intuition develops not so much from solving problems as from visualizing them. Thus the author avoids the definition-theorem-proof style in favor of a structure that encourages the student's geometric intuition of the mathematical results. The presentation of real numbers and functions emphasizes the notion of linearity. Consequently, linear algebra and matrix analysis are integrated into the presentation of the calculus of functions of several variables. The book concludes with a chapter on classical programming, and one on nonlinear and linear programming. This textbook will be of particular interest and value to graduate and senior undergraduate students of economics, because each major mathematical idea is related to an example of its use in economics.

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.

`...an interesting and original contribution to the realist argument' The Times Higher Education Supplement.

It has been quite a challenge for econometricians to model economies in transition. There is no textbook at hand to master that task. Economic theory cannot be applied without adaptations to the characteristic change of a whole economic system. Regression analysis, taking into account past economic development only, is of limited use for the econometrician. Having econometric models at hand would be very helpful for an active economic policy to guide the transition process. Various scenarios representing strategies could be simulated in their consequences to the economy. The best alternative in respect to the government's objectives could be chosen. This very situation has born the idea of co-operation between L6dz and Frankfurt in 1990. There are problems of this kind in Poland and in Germany. The German situation is somewhat better than that of Poland as a relatively small centrally planned economy is being united with a substantial social market economy taking over a lot of the burden of the former mismanagement. Thus, it might be possible to share the experience in modelling the united Germany and preparing forecasts with the Polish model builders. In addition, it would be prOfitable for both model establishing teams to link their models in order to improve the forecasting potential. Moreover, the Polish partner has a broad national and international experience in econometric model building which makes co-operation smooth and fruitful. His experience in modelling countries with a centrally planned economy would also help to master the transition problems.

In the recent years, the study of cointegrated time series and the use of error correction models have become extremely popular in the econometric literature. This book provides an analysis of the notion of (weak) exogeneity, which is necessary to sustain valid inference in sub-systems, inthe framework of error correction models (ECMs). In many practical situations, the applied econometrician wants to introduce "structure" on his/her model in order to get economically meaningful coefficients. For thispurpose, ECMs in structural form provide an appealing framework, allowing the researcher to introduce (theoretically motivated) identification restrictions on the long run relationships. In this case, the validity of the inference will depend on a number of conditions which are investigated here. In particular, we point out that orthogonality tests, often used to test for weak exogeneity or for general misspecification, behave poorly in finite samples and are often not very useful in cointegrated systems.

This book describes a series of laboratory experiments (with a total of 167 independent subjects) on forecasting behavior. In all experiments, the time series to be forecasted was generated by an abstract econometric model involving two or three artificial exogenous variables. This designprovides an optimal background for rational expectations and least-squares learning. As expected, these hypotheses do not explain observed forecasting behavior satisfactorily. Some phenomena related to this lack of rationality are studied: Concentration on changes rather than levels, underestimation of changes and overvaluation of volatile exogenous variables. Some learning behavior is observed. Finally, some aspects of individual forecasts such as prominence of "round" number, dispersion, etc., are studied.

The book is an in-depth review of the theory and empirics of the demand for money and other financial assets. The different theoretical approaches to the portfolio choice problem are described, together with an up-to-date survey of the results obtained from empirical studies of asset choice behaviour. Both single-equation studies and the more complete multi-asset portfolio models, are analysed.

The main theorem of Linear Programming Duality, relating a "pri- mal" Linear Programming problem to its "dual" and vice versa, can be seen as a statement about sign patterns of vectors in complemen- tary subspaces of Rn. This observation, first made by R.T. Rockafellar in the late six- ties, led to the introduction of certain systems of sign vectors, called "oriented matroids". Indeed, when oriented matroids came into being in the early seventies, one of the main issues was to study the fun- damental principles underlying Linear Progra.mrning Duality in this abstract setting. In the present book we tried to follow this approach, i.e., rather than starting out from ordinary (unoriented) matroid theory, we pre- ferred to develop oriented matroids directly as appropriate abstrac- tions of linear subspaces. Thus, the way we introduce oriented ma- troids makes clear that these structures are the most general -and hence, the most simple -ones in which Linear Programming Duality results can be stated and proved. We hope that this helps to get a better understanding of LP-Duality for those who have learned about it before und a good introduction for those who have not.

High and persistent unemployment rates in Europe during the eighties gave rise to a lively discussion about the nature and causes of joblessness. Among other sources structural unemployment was blamed for the lack of response of unemployment to increasing aggregate demand. Renewed attention was thus devoted to an analysis of the magnitude and the development of structural unemployment as well to its possi ble determinants. In this literature, the Beveridge curve experienced a resurrection and, at first glance, it seemed to be an appropriate tool to analyse the aforementioned issues. However, it was soon recognized that the Beveridge curve, i. e. the relation between unemployment and vacancies, was anything but stable, thus requiring a care ful distinction between dynamic loops around a (stable?) long-run Beveridge curve and possible shifts due to, say, an increasing mismatch between labor supplied and demanded. The controversy is far from being settled at the time of this writing. This book contains a collection of hitherto unpublished papers which are devoted to a theoretical and econometric analysis of structural unemployment. The papers put considerable emphasis on the question to what extent the Beveridge curve can serve as an adequate tool for such studies. The countries under consideration are Germany and Austria. In what follows a very brief summary of each paper will be outlined. Franz and Siebeck present, at some length, a theoretical and econometric analysis of the Beveridge curve in Germany."

International commodity markets have traditionally attracted the attention of economists, econometricians, and policy makers especially in and following politically tumultuous times. For instance, the primary commodity price boom of 1973/74 and the subsequent period of highly volatile world market prices initiated increased research on commodity markets which quickly focused on possible price stabilization schemes, particularly on buffer stocks. Simultaneously, the issue clearly advanced in priority on the political agenda, such that the United Nations Conference on Trade and Development (UNCTAD) proposed an "Integrated Program for Commodities" (IPC) intended to stabilize the world market prices of ten so-called "core commodities"l (UNCTAD (1974, 1976a), Behrman (1979)). Many developing nations welcomed the IPC almost enthusiastically, but it did not receive more than lukewarm support by major industrialized countries, apparently due to the experience with some thirty international commodity agreements past World War II2. Critical evaluations have, among others, been presented by McNicol (1978), Gordon-Ashworth (1984), and Macbean & Nguyen (1987). The most detailed of these studies is Gordon-Ashworth's, who concludes that "on balance ... the performance of international commodity agreements has been too unreliable and their distributive effects too uneven to secure the development goals that have been set" (1984, p. 284)3. Consequently, the IPC turned out to be quite controversial a topic on the UNCTAD's 1976 meeting in Nairobi and has not been able to gain any impetus since. lThese were cocoa, coffee, copper, cotton, jute, rubber, sisal, sugar, tea, and tin.