The index of an equilibrium in a game gives information about the "stability" of the equilibrium, for example with respect to game dynamics. Unfortunately, index theory is often very technical. This book presents a new geometric construction that visualises the index in an intuitive way. For example, a 3A-n game, for any n, can be represented by a figure in the plane, from which one can read off any equilibrium, and its index as a geometric orientation. With this insight, the index can be characterised in strategic terms alone. Moreover, certain "hyperstable" equilibrium components are seen to have nonzero index. The construction gives an elementary proof that two-player games have a Nash equilibrium, and, in an unusual direction, the powerful fixed point theorem of Brouwer.

Valuing portfolios of options embedded in investment decisions is arguably one of the most important and challenging problems in real options and corporate ?nance in general. Although the problem is common and vitally important in the value creation process of almost any corporation, it has not yet been satisfactorily addressed. It is key for any corporation facing strategic resource allocation decisions, be it a pharmaceutical ?rm valuing and managing its pipeline of drugs, a telecom company having to select a set of technological alternatives, a venture capital or private equity ?rm investing in a portfolio of ventures, or any company allocating resources. Portfolios of real options typically interact such that the value of the whole differs from the sum of the separate parts. Thus one must address and value the particular con?guration of options embedded in a speci?c situation, taking into account the con?guration of other options already present in the portfolio, which in turn depends on the correlation struc ture among the various underlying assets and the strategic dependencies among the options themselves (e. g. , mutual exclusivity, strategic additiv ity, compoundness, complementarity etc. ). In that sense, optimal decisions also depend on past option exercise decisions by management and organi zational capabilities put in place in the past.

Most of the existing portfolio selection models are based on the probability theory. Though they often deal with the uncertainty via probabilistic - proaches, we have to mention that the probabilistic approaches only partly capture the reality. Some other techniques have also been applied to handle the uncertainty of the ?nancial markets, for instance, the fuzzy set theory [Zadeh (1965)]. In reality, many events with fuzziness are characterized by probabilistic approaches, although they are not random events. The fuzzy set theory has been widely used to solve many practical problems, including ?nancial risk management. By using fuzzy mathematical approaches, quan- tative analysis, qualitative analysis, the experts’ knowledge and the investors’ subjective opinions can be better integrated into a portfolio selection model. The contents of this book mainly comprise of the authors’ research results for fuzzy portfolio selection problems in recent years. In addition, in the book, the authors will also introduce some other important progress in the ?eld of fuzzy portfolio optimization. Some fundamental issues and problems of po- folioselectionhavebeenstudiedsystematicallyandextensivelybytheauthors to apply fuzzy systems theory and optimization methods. A new framework for investment analysis is presented in this book. A series of portfolio sel- tion models are given and some of them might be more e?cient for practical applications. Some application examples are given to illustrate these models by using real data from the Chinese securities markets.

This book presents in detail methodologies for the Bayesian estimation of sing- regime and regime-switching GARCH models. These models are widespread and essential tools in n ancial econometrics and have, until recently, mainly been estimated using the classical Maximum Likelihood technique. As this study aims to demonstrate, the Bayesian approach o ers an attractive alternative which enables small sample results, robust estimation, model discrimination and probabilistic statements on nonlinear functions of the model parameters. The author is indebted to numerous individuals for help in the preparation of this study. Primarily, I owe a great debt to Prof. Dr. Philippe J. Deschamps who inspired me to study Bayesian econometrics, suggested the subject, guided me under his supervision and encouraged my research. I would also like to thank Prof. Dr. Martin Wallmeier and my colleagues of the Department of Quantitative Economics, in particular Michael Beer, Roberto Cerratti and Gilles Kaltenrieder, for their useful comments and discussions. I am very indebted to my friends Carlos Ord as Criado, Julien A. Straubhaar, J er ^ ome Ph. A. Taillard and Mathieu Vuilleumier, for their support in the elds of economics, mathematics and statistics. Thanks also to my friend Kevin Barnes who helped with my English in this work. Finally, I am greatly indebted to my parents and grandparents for their support and encouragement while I was struggling with the writing of this thesis.

Dynamic oligopolistic competition has implications both for the strategic management of firms and for the design of an effective competition policy. Consequently, the present book considers the issue from a private and social perspective. It discusses the potential pro- and anticollusive effects of long-term business strategies, especially for cooperation and reinvestment in production, financing and management compensation, in markets with fluctuating demand. The method of supergame theory is applied to integrate long-run decisions and different types of demand into the analysis. Aside from its contributions to the theoretical literature, the book provides valuable insights into the design of competition policy. The observed development of prices is an indicator of the extent of collusion in the market and can thereby be used to assess antitrust regulation in certain business areas, and to focus the resources of competition authorities on markets where conditions are conducive to collusion.

The author derives an efficient and accurate pricing tool for interest-rate derivatives within a Fourier-transform based pricing approach, which is generally applicable to exponential-affine jump-diffusion models.

This book presents a macroeconomic dynamic model à la Solow-Swan, including the market for labor, in a discrete time structure. The model is expanded to include expenditure on R&D and public expenditure on infrastructure. For each of the three models the results are shown in time series figures, which demonstrate that even small changes in the parameters produce responses in the time behavior of the main variables: from steady growth, to regular cycles, to chaotic-like time paths.

This study investigates the dynamic welfare effects of exposure to trade in a new trade model, which is extended by firm heterogeneity. It is analyzed under which conditions exposure to trade with firm heterogeneity increases or decreases steady state welfare of a country. It uses a new trade model to explore which country-specific conditions give rise to horizontal or vertical multinational activity. Finally, it combines the Heckscher-Ohlin model and a new trade model with horizontal multinational firms.

This volume consists of selected papers presented at the Ninth International Conference on Computer-Aided Scheduling of Public Transport. Coverage includes the use of computer-aided methods and operations research techniques to improve: information management; network and route planning; vehicle and crew scheduling and rostering; vehicle monitoring and management; and practical experience with scheduling and public transport planning methods.

1. 1 The Area of Research In this thesis, we will investigate the 'market-conform' pricing of newly issued contingent claims. A contingent claim is a derivative whose value at any settlement date is determined by the value of one or more other underlying assets, e. g. , forwards, futures, plain-vanilla or exotic options with European or American-style exercise features. Market-conform pricing means that prices of existing actively traded securities are taken as given, and then the set of equivalent martingale measures that are consistent with the initial prices of the traded securities is derived using no-arbitrage arguments. Sometimes in the literature other expressions are used for 'market-conform' valuation - 'smile-consistent' valuation or 'fair-market' valuation - that describe the same basic idea. The seminal work by Black and Scholes (1973) (BS) and Merton (1973) mark a breakthrough in the problem of hedging and pricing contingent claims based on no-arbitrage arguments. Harrison and Kreps (1979) provide a firm mathematical foundation for the Black-Scholes- Merton analysis. They show that the absence of arbitrage is equivalent to the existence of an equivalent martingale measure. Under this mea sure the normalized security price process forms a martingale and so securities can be valued by taking expectations. If the securities market is complete, then the equivalent martingale measure and hence the price of any security are unique.