Considerable work has been done on chaotic dynamics in the field of economic growth and dynamic macroeconomic models during the last two decades. This book considers numerous new developments: introduction of infrastructure in growth models, heterogeneity of agents, hysteresis systems, overlapping models with "pay-as-you-go" systems, keynesian approaches with finance considerations, interactions between relaxation cycles and chaotic dynamics, methodological issues, long memory processes and fractals... A volume of contributions which shows the relevance and fruitfulness of non-linear analysis for the explanation of complex dynamics in economic systems.

Considerable work has been done on chaotic dynamics in the field of economic growth and dynamic macroeconomic models during the last two decades. This book considers numerous new developments: introduction of infrastructure in growth models, heterogeneity of agents, hysteresis systems, overlapping models with "pay-as-you-go" systems, keynesian approaches with finance considerations, interactions between relaxation cycles and chaotic dynamics, methodological issues, long memory processes and fractals... A volume of contributions which shows the relevance and fruitfulness of non-linear analysis for the explanation of complex dynamics in economic systems.

Optimal growth theory studies the problem of efficient resource allocation over time, a fundamental concern of economic research. Since the 1970s, the techniques of nonlinear dynamical systems have become a vital tool in optimal growth theory, illuminating dynamics and demonstrating the possibility of endogenous economic fluctuations. Kazuo Nishimura's seminal contributions on business cycles, chaotic equilibria and indeterminacy have been central to this development, transforming our understanding of economic growth, cycles, and the relationship between them. The subjects of Kazuo's analysis remain of fundamental importance to modern economic theory. This book collects his major contributions in a single volume. Kazuo Nishimura has been recognized for his contributions to economic theory on many occasions, being elected fellow of the Econometric Society and serving as an editor of several major journals. Chapter “Introduction” is available open access under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License via link.springer.com.

This interdisciplinary book argues that the economy has an underlying non-linear structure and that business cycles are endogenous, which allows a greater explanatory power with respect to the traditional assumption that dynamics are stochastic and shocks are exogenous. The first part of this work is formal-methodological and provides the mathematical background needed for the remainder, while the second part presents the view that signal processing involves construction and deconstruction of information and that the efficacy of this process can be measured. The third part focuses on economics and provides the related background and literature on economic dynamics and the fourth part is devoted to new perspectives in understanding nonlinearities in economic dynamics: growth and cycles. By pursuing this approach, the book seeks to (1) determine whether, and if so where, common features exist, (2) discover some hidden features of economic dynamics, and (3) highlight specific indicators of structural changes in time series. Accordingly, it is a must read for everyone interested in a better understanding of economic dynamics, business cycles, econometrics and complex systems, as well as non-linear dynamics and chaos theory.

Writing a book is not possible without the generous input of many people. It is a pleasure to have the opportunity to thank at least some of these people. Prof. Dr. Jochen Michaelis, the supervisor of my dissertation, taught me how to do economic analysis and initiated my interest in labour market is sues. Discussions with him have always been enlightening and have greatly improved the analysis in this book. Moreover, he always encouraged me when I experienced a slump in my motivation. He never lost his calmness and good temper, not even in situations when my need for discussion must have been bothering him. Thanks for that Jochen. I'm indebted to Prof. Dr. Peter Weise for taking over the job as the sec ond referee of my thesis. He gave very valuable comments and sacrificed his christmas holiday to write the referee report as fast as possible. I also want to thank Prof. Stefan Voigt and Prof. Dr. Reinhold Kosfeld, the other two members of the dissertation committee, for the discussion during the defence of the thesis.

Unemployment in Open Economies studies how domestic labour markets are influenced by a changing international environment. It combines the recently developed search and matching models with standard models of international trade. By this method, the reader gains new insights in the ongoing debate on how globalisation can affect unemployment. The author develops a collection of models showing that globalisation can be one reason for long-known and well-documented phenomenons on the labour market. She puts emphasis on country differences by studying the role of individual risk behavior and the wage setting on the unemployment level.

Increasing customer requirements, product variety, and market competition demand for service and cost improvements by model based inventory control in supply chains. The book presents approaches for safety stock determination in manufacturing and logistics networks. Most of the existing literature provides methods for very specific types of supply networks. The approach presented in this book follows a material flow philosophy that allows for several extensions of the basic models and therefore offers a wide applicability within decision support systems. Models for several types of problems and network structures are presented and analyzed to develop efficient optimization algorithms and heuristics.

From a technical point of view, the celebrated Black and Scholes option pricing formula was originally developed using a separation of variables technique. However, already Merton mentioned in his seminal 1973 pa per, that it could have been developed by using Fourier transforms as well. Indeed, as is well known nowadays, Fourier transforms are a rather convenient solution technique for many models involving the fundamental partial differential equation of financial economics. It took the community nearly another twenty years to recognize that Fourier transform is even more useful, if one applies it to problems in financial economics without seeking an explicit analytical inverse trans form. Heston (1993) probably was the first to demonstrate how to solve a stochastic volatility option pricing model quasi analytically using the characteristic function of the problem, which is nothing else than the Fourier transform of the underlying Arrow /Debreu-prices, and doing the inverse transformation numerically. This opened the door for a whole bunch of new closed form solutions in the transformed Fourier space and still is one of the most active research areas in financial economics.

Variational inequalities proved to be a very useful and powerful tool for in vestigation and solution of many equilibrium type problems in Economics, Engineering, Operations Research and Mathematical Physics. In fact, varia tional inequalities for example provide a unifying framework for the study of such diverse problems as boundary value problems, price equilibrium prob lems and traffic network equilibrium problems. Besides, they are closely re lated with many general problems of Nonlinear Analysis, such as fixed point, optimization and complementarity problems. As a result, the theory and so lution methods for variational inequalities have been studied extensively, and considerable advances have been made in these areas. This book is devoted to a new general approach to constructing solution methods for variational inequalities, which was called the combined relax ation (CR) approach. This approach is based on combining, modifying and generalizing ideas contained in various relaxation methods. In fact, each com bined relaxation method has a two-level structure, i.e., a descent direction and a stepsize at each iteration are computed by finite relaxation procedures.

This book provides a thorough analysis of scheduling problems that arise in a flexible manufacturing environment with scarce resource supply. Generalizations of the famous job shop scheduling problem are discussed. As a basic and common technique for solving these problems constraint propagation is applied in various solution methods. The effectiveness of constraint propagation is demonstrated by the solution of a high number of benchmark problem instances.