Most of the observable phenomena in the empirical sciences are of multivariate nature. This book presents the tools and concepts of multivariate data analysis with a strong focus on applications. The text is devided into three parts. The first part is devoted to graphical techniques describing the distributions of the involved variables. The second part deals with multivariate random variables and presents from a theoretical point of view distributions, estimators and tests for various practical situations. The last part covers multivariate techniques and introduces the reader into the wide basket of tools for multivariate data analysis. The text presents a wide range of examples and 228 exercises.

The three decades which have followed the publication of Heinz Neudecker's seminal paper `Some Theorems on Matrix Differentiation with Special Reference to Kronecker Products' in the Journal of the American Statistical Association (1969) have witnessed the growing influence of matrix analysis in many scientific disciplines. Amongst these are the disciplines to which Neudecker has contributed directly - namely econometrics, economics, psychometrics and multivariate analysis.

Computer simulations of economic systems are slowly gaining ground within the economic profession. However, such a process is hindered by a lack of communication among researchers who do not share a common language. For its object-oriented structure and its versatility, Swarm has the necessary characteristics to become a credible universal language of agent-based simulations.

This book assesses the main interrelationships between economic growth processes, life cycle sustainability assessment approaches, and new technologies in the framework of digital transition. In other words, it aims to highlight how sustainability assessment methodologies and artificial intelligence can better support different actors for more sustainable economic growth. Readers of the book would benefit from diverse perspectives on the contributions of evaluation methodologies and digital technologies to more sustainable economic growth. This is important especially for students, policymakers and public institutions. Economic growth is analysed using the concepts of sigma and beta convergence from neoclassical theory and the Verdoorn law of Keynesian development. For sustainability assessments, the book considers methodologies associated with social life cycle assessment and life cycle cost analysis. In the context of digital technologies, special emphasis is given to machine and deep learning approaches.

This concise primer (based on lectures given at summer schools on complex systems and on a masters degree course in complex systems modeling) will provide graduate students and newcomers to the field with the basic knowledge of the concepts and methods of statistical physics and its potential for application to interdisciplinary topics.

The climate is changing, bringing with it increasing natural disasters around the world. The progress of societies lies in their ability to adapt to the new climatic conditions. Effective climate-adaptation strategies must be based in the sound analysis of the costs of the disasters, as well as the potential benefits and beneficiaries of adaptation strategies. This book offers an appraisal method to capture the total economic costs of flooding events: the Multiregional Flood Footprint Analysis. It captures the economic costs directly caused by physical destruction, and disruptive implications in production propagated through inter-industrial linkages in the current context of a global economy. The proposed method uses the fundamentals of the Input-Output analysis (IOA) in a multiregional dimension. It concludes that damages from natural disasters in one part of the globe may affect many economic sectors in the rest of the world, increasing the need for global adaptation strategies.

In this volume are papers written by students and co-authors of Stanley Reiter. The collection reflects to some extent the range of his interests and intellectual curiosity. He has published papers in statistics, manage­ ment science, international trade, and welfare economics. He co-authored early papers in economic history and is reported to be largely responsible for giving the field its name of Cliometrics. He helped initiate, nurture and establish the area of economics now known as mechanism design which studies information decentralization, incentives, computational complexity and the dynamics of decentralized interactions. The quality, craft, depth, and innovative nature of his work has always been at an exceptionally high level. Stan has had a strong and important direct effect on many students at Purdue University and Northwestern University. He created and taught a course which all of his students have both dreaded and respected. Using the Socratic method in remarkably effective ways to teach theory skills, he has guided, prodded, and encouraged us to levels we did not think we were capable of. Some of his students are represented in this volume. But even those whose careers took directions other than mathematical economics still consider that training to be an important component of their success. Stan's students include department chairmen, business executives, Deans, a Secretary of the Air Force, and a College President. His guidance has been necessary and fundamental to whatever successes we have had.

The English edition differs only slightly from the Russian original. The main struc­ tural difference is that all the material on the theory of finite noncooperative games has been collected in Chapter 2, with renumbering of the material of the remain­ ing chapters. New sections have been added in this chapter: devoted to general questions of equilibrium theory in nondegenerate games, subsections 3.9-3.17, by N.N. Vorob'ev, Jr.; and § 4, by A.G. Chernyakov; and § 5, by N.N. Vorob'ev, Jr., on the computational complexity of the process of finding equilibrium points in finite games. It should also be mentioned that subsections 3.12-3.14 in Chapter 1 were written by E.B. Yanovskaya especially for the Russian edition. The author regrets that the present edition does not reflect the important game-theoretical achievements presented in the splendid monographs by E. van Damme (on the refinement of equilibrium principles for finite games), as well as those by J.e. Harsanyi and R. Selten, and by W. Giith and B. Kalkofen (on equilibrium selection).

Today many economists, engineers and mathematicians are familiar with linear programming and are able to apply it. This is owing to the following facts: during the last 25 years efficient methods have been developed; at the same time sufficient computer capacity became available; finally, in many different fields, linear programs have turned out to be appropriate models for solving practical problems. However, to apply the theory and the methods of linear programming, it is required that the data determining a linear program be fixed known numbers.

This textbook gives a comprehensive introduction to stochastic processes and calculus in the fields of finance and economics, more specifically mathematical finance and time series econometrics. Over the past decades stochastic calculus and processes have gained great importance, because they play a decisive role in the modeling of financial markets and as a basis for modern time series econometrics. Mathematical theory is applied to solve stochastic differential equations and to derive limiting results for statistical inference on nonstationary processes.

When Murat Sertel asked us whether we would be interested in organizing a special issue of the Review of Economic Design on the formation of networks and groups, we were happy to accept because of the growing research on this important topic. We were also pleasantly surprised at the response to our request for submissions to the special issue, receiving a much larger number of sub­ missions than we had anticipated. In the end we were able to put together two special issues of insightful papers on this topic. Given the growing interest in this topic, we also decided (with encouragement from Murat) to combine the special issues in the form of a book for wider dissemination. However, once we had decided to edit the book, it was natural to move beyond the special issue to include at least some of the papers that have been influential in the literature on the formation of networks. These papers were published in other journals, and we are very grateful to the authors as well as the journals for permission to include these papers in the book.

Financial Markets Theory presents classical asset pricing theory, a theory composed of milestones such as portfolio selection, risk aversion, fundamental asset pricing theorem, portfolio frontier, CAPM, CCAPM, APT, the Modigliani-Miller Theorem, no arbitrage/risk neutral evaluation and information in financial markets. Starting from an analysis of the empirical tests of the above theories, the author provides a discussion of the most recent literature, pointing out the main advancements within classical asset pricing theory and the new approaches designed to address open problems (e.g. behavioural finance).

A lot of economic problems can formulated as constrained optimizations and equilibration of their solutions. Various mathematical theories have been supplying economists with indispensable machineries for these problems arising in economic theory. Conversely, mathematicians have been stimulated by various mathematical difficulties raised by economic theories. The series is designed to bring together those mathematicians who were seriously interested in getting new challenging stimuli from economic theories with those economists who are seeking for effective mathematical tools for their researchers.

Economic Modeling Using Artificial Intelligence Methods examines the application of artificial intelligence methods to model economic data. Traditionally, economic modeling has been modeled in the linear domain where the principles of superposition are valid. The application of artificial intelligence for economic modeling allows for a flexible multi-order non-linear modeling. In addition, game theory has largely been applied in economic modeling. However, the inherent limitation of game theory when dealing with many player games encourages the use of multi-agent systems for modeling economic phenomena.

Perceiving the economy as a complex dynamic system, generates a need for new tools for its study. As a constructive simulation method, Agent-Based Computational Economics (ACE) has in recent years proven its strength and extensive applicability. Fields of study are widely spread within economics, with a cluster around financial markets. This book is based on communications given at AE’2006 (Aalborg, Denmark) – the second symposium on Artificial Economics, and covers both wellknown questions of economics, like the existence of market efficiency, as well as new questions raised by the new tools, for example questions related to networks of social interaction.