Long-rangedependent, or long-memory, time seriesarestationarytime series displaying a statistically signi?cant dependence between very distant obs- vations. We formalize this dependence by assuming that the autocorrelation function of these stationary series decays very slowly, hyperbolically, as a function of the time lag. Many economic series display these empirical features: volatility of asset prices returns, future interest rates, etc. There is a huge statistical literature on long-memory processes, some of this research is highly technical, so that it is cited, but often misused in the applied econometrics and empirical e- nomics literature. The ?rst purpose of this book is to present in a formal and pedagogical way some statistical methods for studying long-range dependent processes. Furthermore, the occurrence of long-memory in economic time series might be a statistical artefact as the hyperbolic decay of the sample autoc- relation function does not necessarily derive from long-range dependent p- cesses. Indeed, the realizations of non-homogeneous processes, e.g., switching regime and change-point processes, display the same empirical features. We thus also present in this book recent statistical methods able to discriminate between the long-memory and change-point alternatives. Going beyond the purely statistical analysis of economic series, it is of interest to determine which economic mechanisms are generating the strong dependence properties of economic series, whether they are genuine, or spu- ous. The regularities of the long-memory and change-point properties across economic time series, e.g., common degree of long-range dependence and/or common change-points, suggest the existence of a common economic cause

Modern option pricing theory was developed in the late sixties and early seventies by F. Black, R. e. Merton and M. Scholes as an analytical tool for pricing and hedging option contracts and over-the-counter warrants. How ever, already in the seminal paper by Black and Scholes, the applicability of the model was regarded as much broader. In the second part of their paper, the authors demonstrated that a levered firm's equity can be regarded as an option on the value of the firm, and thus can be priced by option valuation techniques. A year later, Merton showed how the default risk structure of cor porate bonds can be determined by option pricing techniques. Option pricing models are now used to price virtually the full range of financial instruments and financial guarantees such as deposit insurance and collateral, and to quantify the associated risks. Over the years, option pricing has evolved from a set of specific models to a general analytical framework for analyzing the production process of financial contracts and their function in the financial intermediation process in a continuous time framework. However, very few attempts have been made in the literature to integrate game theory aspects, i. e. strategic financial decisions of the agents, into the continuous time framework. This is the unique contribution of the thesis of Dr. Alexandre Ziegler. Benefiting from the analytical tractability of contin uous time models and the closed form valuation models for derivatives, Dr."

The present volume contains the proceedings of the workshop on "Minimax Theory and Applications" that was held during the week 30 September - 6 October 1996 at the "G. Stampacchia" International School of Mathematics of the "E. Majorana" Centre for Scientific Cul ture in Erice (Italy) . The main theme of the workshop was minimax theory in its most classical meaning. That is to say, given a real-valued function f on a product space X x Y, one tries to find conditions that ensure the validity of the equality sup inf f(x, y) = inf sup f(x, y). yEY xEX xEX yEY This is not an appropriate place to enter into the technical details of the proofs of minimax theorems, or into the history of the contribu tions to the solution of this basic problem in the last 7 decades. But we do want to stress its intrinsic interest and point out that, in spite of its extremely simple formulation, it conceals a great wealth of ideas. This is clearly shown by the large variety of methods and tools that have been used to study it. The applications of minimax theory are also extremely interesting. In fact, the need for the ability to "switch quantifiers" arises in a seemingly boundless range of different situations. So, the good quality of a minimax theorem can also be judged by its applicability. We hope that this volume will offer a rather complete account of the state of the art of the subject."

The Bachelier Society for Mathematical Finance held its first World Congress in Paris last year, and coincided with the centenary of Louis Bacheliers thesis defence. In his thesis Bachelier introduces Brownian motion as a tool for the analysis of financial markets as well as the exact definition of options. The thesis is viewed by many the key event that marked the emergence of mathematical finance as a scientific discipline. The prestigious list of plenary speakers in Paris included two Nobel laureates, Paul Samuelson and Robert Merton, and the mathematicians Henry McKean and S.R.S. Varadhan. Over 130 further selected talks were given in three parallel sessions. .

This monograph covers one of the divisions of mathematical theory of control which examines moving objects functionating under conflict and uncertainty conditions. To identify this range of problems we use the term "conflict con trolled processes," coined in recent years. As the name itself does not imply the type of dynamics (difference, ordinary differential, difference-differential, integral, or partial differential equations) the differential games falI within its realms. The problems of search and tracking moving objects are also referred to the field of conflict controlled process. The contents of the monograph is confined to studying classical pursuit-evasion problems which are central to the theory of conflict controlled processes. These problems underlie the theory and are of considerable interest to researchers up to now. It should be noted that the methods of "Line of Sight," "Parallel Pursuit," "Proportional N avigation,""Modified Pursuit" and others have been long and well known among engineers engaged in design of rocket and space technology. An abstract theory of dynamic game problems, in its turn, is based on the methods originated by R. Isaacs, L. S. Pontryagin, and N. N. Krasovskii, and on the approaches developed around these methods. At the heart of the book is the Method of Resolving Functions which was realized within the class of quasistrategies for pursuers and then applied to the solution of the problems of "hand-to-hand," group, and succesive pursuit."

The fourth edition is augmented by more than 70 new formulas. In particular, we have included some key concepts and results from trade theory, games of incomplete information and combinatorics. In addition there are scattered additions of new formulas in many chapters. Again we are indebted to a number of people who has suggested corrections, - provements and new formulas. In particular, we would like to thank Jens-Henrik Madsen, Larry Karp, Harald Goldstein, and Geir Asheim. In a reference book, errors are particularly destructive. We hope that readers who ?nd our remaining errors will call them to our attention so that we may purge them from future editions. Oslo and Berkeley, May 2005 Knut Sydsaeter, Arne Strom, Peter Berck From the preface to the third edition Thepracticeofeconomicsrequiresawide-rangingknowledgeofformulasfrommat- matics, statistics, andmathematicaleconomics. Withthisvolumewehopetopresent a formulary tailored to the needs of students and working professionals in economics. In addition to a selection of mathematical and statistical formulas often used by economists, this volume contains many purely economic results and theorems. It containsjusttheformulasandtheminimumcommentaryneededtorelearnthema- ematics involved. We have endeavored to state theorems at the level of generality economists might ?nd useful. In contrast to the economic maxim, "everything is twice more continuously di?erentiable than it needs to be," we have usually listed theregularityconditionsfortheoremstobetrue.Wehopethatwehaveachieveda level of explication that is accurate and useful without being pedantic."

This book introduces the student to numerous modern applications of mathematics in technology. The authors write with clarity and present the mathematics in a clear and straightforward way making it an interesting and easy book to read. Numerous exercises at the end of every section provide practice and reinforce the material in the chapter. An engaging quality of this book is that the authors also present the mathematical material in a historical context and not just the practical one.

Mathematics and Technology is intended for undergraduate students in mathematics, instructors and high school teachers. Additionally, its lack of calculus centricity as well as a clear indication of the more difficult topics and relatively advanced references make it suitable for any curious individual with a decent command of high school math.

Search Theory is one of the original disciplines within the field of Operations Research. It deals with the problem faced by a Searcher who wishes to minimize the time required to find a hidden object, or "target. " The Searcher chooses a path in the "search space" and finds the target when he is sufficiently close to it. Traditionally, the target is assumed to have no motives of its own regarding when it is found; it is simply stationary and hidden according to a known distribution (e. g. , oil), or its motion is determined stochastically by known rules (e. g. , a fox in a forest). The problems dealt with in this book assume, on the contrary, that the "target" is an independent player of equal status to the Searcher, who cares about when he is found. We consider two possible motives of the target, and divide the book accordingly. Book I considers the zero-sum game that results when the target (here called the Hider) does not want to be found. Such problems have been called Search Games (with the "ze- sum" qualifier understood). Book II considers the opposite motive of the target, namely, that he wants to be found. In this case the Searcher and the Hider can be thought of as a team of agents (simply called Player I and Player II) with identical aims, and the coordination problem they jointly face is called the Rendezvous Search Problem.

This volume contains several surveys focused on the ideas of approximate solutions, well-posedness and stability of problems in scalar and vector optimization, game theory and calculus of variations. These concepts are of particular interest in many fields of mathematics. The idea of stability goes back at least to J. Hadamard who introduced it in the setting of differential equations; the concept of well-posedness for minimum problems is more recent (the mid-sixties) and originates with A.N. Tykhonov. It turns out that there are connections between the two properties in the sense that a well-posed problem which, at least in principle, is "easy to solve," has a solution set that does not vary too much under perturbation of the data of the problem, i.e. it is "stable." These themes have been studied in depth for minimum problems and now we have a general picture of the related phenomena in this case. But, of course, the same concepts can be studied in other more complicated situations as, e.g. vector optimization, game theory and variational inequalities. Let us mention that in several of these new areas there is not even a unique idea of what should be called approximate solution, and the latter is at the basis of the definition of well posed problem."

In the first part of this book, we treat interacting and small open economies. We do this from an historical perspective, starting from the Classical model of the gold standard and the specie-flow mechanism and aim to show there that the Dornbusch IS-LM-PC approach, with or without rational expectations, can still be considered as a (if not the) core contribution to contemporaneous open economy macrodynamics, also on the level of structural macroeconometric model building. In the second part we then extend this analysis to the incorporation of more disequilibrium on the real markets, prominent further feedback channels of the macrodynamic literature and integrated macromodel building. We start from the closed economy, consider large open economies in a fixed exchange rate system, small open economies subject to high capital mobility, and finally two large interacting economies like the USA and Euroland. Our macrofounded approach extends and integrates non-market clearing traditions to macrodynamics and can be usefully compared with the New Keynesian approaches which are generally rigorously microfounded, but often much more limited in scope in capturing full market and agent interactions.

Each concept is discussed from the basics and supported by sufficient mathematical background and worked examples.

Suitable for individual or group learning, the book offers numerous end-of-chapter problems for study and review.

Here, two highly experienced authors present an alternative approach to optimal stopping problems. The basic ideas and techniques of the approach can be explained much simpler than the standard methods in the literature on optimal stopping problems. The monograph will teach the reader to apply the technique to many problems in economics and finance, including new ones. From the technical point of view, the method can be characterized as option pricing via the Wiener-Hopf factorization.

Handbook of the Shapley Value contains 24 chapters and a foreword written by Alvin E. Roth, who was awarded the Nobel Memorial Prize in Economic Sciences jointly with Lloyd Shapley in 2012. The purpose of the book is to highlight a range of relevant insights into the Shapley value. Every chapter has been written to honor Lloyd Shapley, who introduced this fascinating value in 1953. The first chapter, by William Thomson, places the Shapley value in the broader context of the theory of cooperative games, and briefly introduces each of the individual contributions to the volume. This is followed by a further contribution from the editors of the volume, which serves to introduce the more significant features of the Shapley value. The rest of the chapters in the book deal with different theoretical or applied aspects inspired by this interesting value and have been contributed specifically for this volume by leading experts in the area of Game Theory. Chapters 3 through to 10 are more focused on theoretical aspects of the Shapley value, Chapters 11 to 15 are related to both theoretical and applied areas. Finally, from Chapter 16 to Chapter 24, more attention is paid to applications of the Shapley value to different problems encountered across a diverse range of fields. As expressed by William Thomson in the Introduction to the book, "The chapters contribute to the subject in several dimensions: Mathematical foundations; axiomatic foundations; computations; applications to special classes of games; power indices; applications to enriched classes of games; applications to concretely specified allocation problems: an ever-widening range, mapping allocation problems into games or implementation." Nowadays, the Shapley value continues to be as appealing as when it was first introduced in 1953, or perhaps even more so now that its potential is supported by the quantity and quality of the available results. This volume collects a large amount of work that definitively demonstrates that the Shapley value provides answers and solutions to a wide variety of problems.

The present third edition of The Statistical Mechanics of Financial Markets is published only four years after the ?rst edition. The success of the book highlights the interest in a summary of the broad research activities on the application of statistical physics to ?nancial markets. I am very grateful to readers and reviewers for their positive reception and comments. Why then prepare a new edition instead of only reprinting and correcting the second edition? The new edition has been signi?cantly expanded, giving it a more pr- tical twist towards banking. The most important extensions are due to my practical experience as a risk manager in the German Savings Banks' As- ciation (DSGV): Two new chapters on risk management and on the closely related topic of economic and regulatory capital for ?nancial institutions, - spectively, have been added. The chapter on risk management contains both the basics as well as advanced topics, e. g. coherent risk measures, which have not yet reached the statistical physics community interested in ?nancial m- kets. Similarly, it is surprising how little research by academic physicists has appeared on topics relating to Basel II. Basel II is the new capital adequacy framework which will set the standards in risk management in many co- tries for the years to come. Basel II is responsible for many job openings in banks for which physicists are extemely well quali?ed. For these reasons, an outline of Basel II takes a major part of the chapter on capital.

Peter Fishburn has had a splendidly productive career that led to path-breaking c- tributions in a remarkable variety of areas of research. His contributions have been published in a vast literature, ranging through journals of social choice and welfare, decision theory, operations research, economic theory, political science, mathema- cal psychology, and discrete mathematics. This work was done both on an individual basis and with a very long list of coauthors. The contributions that Fishburn made can roughly be divided into three major topical areas, and contributions to each of these areas are identi?ed by sections of this monograph. Section 1 deals with topics that are included in the general areas of utility, preference, individual choice, subjective probability, and measurement t- ory. Section 2 covers social choice theory, voting models, and social welfare. S- tion 3 deals with more purely mathematical topics that are related to combinatorics, graph theory, and ordered sets. The common theme of Fishburn's contributions to all of these areas is his ability to bring rigorous mathematical analysis to bear on a wide range of dif?cult problems.

This Festschrift is dedicated to Goetz Trenkler on the occasion of his 65th birthday. As can be seen from the long list of contributions, Goetz has had and still has an enormous range of interests, and colleagues to share these interests with. He is a leading expert in linear models with a particular focus on matrix algebra in its relation to statistics. He has published in almost all major statistics and matrix theory journals. His research activities also include other areas (like nonparametrics, statistics and sports, combination of forecasts and magic squares, just to mention afew). Goetz Trenkler was born in Dresden in 1943. After his school years in East G- many and West-Berlin, he obtained a Diploma in Mathematics from Free University of Berlin (1970), where he also discovered his interest in Mathematical Statistics. In 1973, he completed his Ph.D. with a thesis titled: On a distance-generating fu- tion of probability measures. He then moved on to the University of Hannover to become Lecturer and to write a habilitation-thesis (submitted 1979) on alternatives to the Ordinary Least Squares estimator in the Linear Regression Model, a topic that would become his predominant ?eld of research in the years to come.

Cooperative game theory is a booming research area with many new developments in the last few years. So, our main purpose when prep- ing the second edition was to incorporate as much of these new dev- opments as possible without changing the structure of the book. First, this o?ered us the opportunity to enhance and expand the treatment of traditional cooperative games, called here crisp games, and, especially, that of multi-choice games, in the idea to make the three parts of the monograph more balanced. Second, we have used the opportunity of a secondeditiontoupdateandenlargethelistofreferencesregardingthe threemodels of cooperative games. Finally, we have bene?ted fromthis opportunity by removing typos and a few less important results from the ?rst edition of the book, and by slightly polishing the English style and the punctuation, for the sake of consistency along the monograph. The main changes are: (1) Chapter 3 contains an additional section, Section 3. 3, on the - erage lexicographic value, which is a recent one-point solution concept de?ned on the class of balanced crisp games. (2) Chapter 4 is new. It o?ers a brief overview on solution c- cepts for crisp games from the point of view of egalitarian criteria, and presents in Section 4. 2 a recent set-valued solution concept based on egalitarian considerations, namely the equal split-o? set. (3)Chapter5isbasicallyanenlargedversionofChapter4ofthe?rst edition because Section 5. 4 dealing with the relation between convex games and clan games with crisp coalitions is new.

In June of 2002, over 500 professors, students and researchers met in Boston, Massachusetts for the Fourth International Conference on Complex Systems. The attendees represented a remarkably diverse collection of fields: biology, ecology, physics, engineering, computer science, economics, psychology and sociology, The goal of the conference was to encourage cross-fertilization between the many disciplines represented and to deepen understanding of the properties common to all complex systems.

This volume contains 43 papers selected from the more than 200 presented at the conference. Topics include: cellular automata, neurology, evolution, computer science, network dynamics, and urban planning.

About NECSI: For over 10 years, The New England Complex Systems Institute (NECSI) has been instrumental in the development of complex systems science and its applications. NECSI conducts research, education, knowledge dissemination, and community development around the world for the promotion of the study of complex systems and its application for the betterment of society. NECSI hosts the International Conference on Complex Systems and publishes the NECSI Book Series in conjunction with Springer Publishers.

ALI MINAI is an Affiliate of the New England Complex Systems Institute and an Associate Professor in the Department of Electrical and Computer Engineering and Computer Science at the University of Cincinnati.

YANEER BAR-YAM is President and founder of the New England Complex Systems Institute. He is the author of Dynamics of Complex Systems and Making Things Work: Solving Complex Problems in a Complex World.

Stochastic optimization problems arise in decision-making problems under uncertainty, and find various applications in economics and finance. On the other hand, problems in finance have recently led to new developments in the theory of stochastic control. This volume provides a systematic treatment of stochastic optimization problems applied to finance by presenting the different existing methods: dynamic programming, viscosity solutions, backward stochastic differential equations, and martingale duality methods. The theory is discussed in the context of recent developments in this field, with complete and detailed proofs, and is illustrated by means of concrete examples from the world of finance: portfolio allocation, option hedging, real options, optimal investment, etc. This book is directed towards graduate students and researchers in mathematical finance, and will also benefit applied mathematicians interested in financial applications and practitioners wishing to know more about the use of stochastic optimization methods in finance.

This monograph is an introduction to some aspects of stochastic analysis in the framework of normal martingales, in both discrete and continuous time. The text is mostly self-contained, except for Section 5.7 that requires some background in geometry, and should be accessible to graduate students and researchers having already received a basic training in probability. Prereq- sites are mostly limited to a knowledge of measure theory and probability, namely?-algebras,expectations,andconditionalexpectations.Ashortint- duction to stochastic calculus for continuous and jump processes is given in Chapter 2 using normal martingales, whose predictable quadratic variation is the Lebesgue measure. There already exists several books devoted to stochastic analysis for c- tinuous di?usion processes on Gaussian and Wiener spaces, cf. e.g. [51], [63], [65], [72], [83], [84], [92], [128], [134], [143], [146], [147]. The particular f- ture of this text is to simultaneously consider continuous processes and jump processes in the uni?ed framework of normal martingales.

Andreas Schertzinger identifies determinants of successful transactions, such as transaction timing and diversifying transaction strategy, through a multivariate statistical analysis. Two case studies illustrate success factors specifically related to the conduct of transactions in greater detail.

For the last few years researchers in business administration have increasingly become aware of the central role of small and medium enterprises for the prosperity of an economy. As a consequence, "entrepeneurship" has grown a most relevant sub-discipline in business administration. This special issue focuses on the specific problems in the field of finance that are essential for small and medium enterprises. The articles offer an excellent overview of research questions lying at the very heart of entrepreneurial finance and thus may serve as the starting point for further interesting investigations.

What does the 2000 US Presidential Election have in common with selecting a textbook for a calculus course in your department? Was Ralph Nader's influence on the election of George W. Bush greater than the now-famous chads? In this book, Don Saari analyzes these questions, placing them in the larger context of voting systems in general. His analysis shows that the fundamental problems with the 2000 presidential election are not with the courts, recounts or defective ballots, but are caused by the very way Americans vote for president This expository book shows how mathematics can help to identify and characterize a disturbingly large number of paradoxical situations that result from the choice of a voting procedure. Moreover, rather than being able to dismiss them as anomalies, the likelihood of a dubious election result is surprisingly large. These consequences indicate that election outcomes - whether for president, the site of the next Olympics, the chair of a university department, or a prize winner-can differ from what the voters really wanted. They show that by using an inadequate voting procedure, we can, inadvertently, choose badly. To add to the difficulties, it turns out

Elfi Ettinger focuses her research on how financial consultants perceive, explain, and interpret their commitment at work based on their collective reality of actions and behavior. She analyzes which organizational performance variables consultants associate with their commitment at work, and how consultants' commitment behavior is linked with organizational performance.

What motives underlie the ways humans interact socially? Are these the same for all societies? Are these part of our nature, or influenced by our environments? Over the last decade, research in experimental economics has emphatically falsified the textbook representation of Homo economicus. Hundreds of experiments suggest that people care not only about their own material payoffs, but also about such things as fairness, equity, and reciprocity. However, this research left fundamental questions unanswered: Are such social preferences stable components of human nature, or are they modulated by economic, social, and cultural environments? Until now, experimental research could not address this question because virtually all subjects had been university students. Combining ethnographic and experimental approaches to fill this gap, this book breaks new ground in reporting the results of a large cross-cultural study aimed at determining the sources of social (non-selfish) preferences that underlie the diversity of human sociality. In this study, the same experiments carried out with university students were performed in fifteen small-scale societies exhibiting a wide variety of social, economic, and cultural conditions. The results show that the variation in behaviour is far greater than previously thought, and that the differences between societies in market integration and the importance of cooperation explain a substantial portion of this variation, which individual-level economic and demographic variables could not. The results also trace the extent to which experimental play mirrors patterns of interaction found in everyday life. The book includes a succinct but substantive introduction to the use of game theory as an analytical tool, and to its use in the social sciences for the rigorous testing of hypotheses about fundamental aspects of social behaviour outside artificially constructed laboratories. The editors also summarize the results of the fifteen case studies in a suggestive chapter about the scope of the project.