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This thesis summarizes most of my recent research in the field of portfolio optimization. The main topics which I have addressed are portfolio problems with stochastic interest rates and portfolio problems with defaultable assets. The starting point for my research was the paper "A stochastic control ap proach to portfolio problems with stochastic interest rates" (jointly with Ralf Korn), in which we solved portfolio problems given a Vasicek term structure of the short rate. Having considered the Vasicek model, it was obvious that I should analyze portfolio problems where the interest rate dynamics are gov erned by other common short rate models. The relevant results are presented in Chapter 2. The second main issue concerns portfolio problems with default able assets modeled in a firm value framework. Since the assets of a firm then correspond to contingent claims on firm value, I searched for a way to easily deal with such claims in portfolio problems. For this reason, I developed the elasticity approach to portfolio optimization which is presented in Chapter 3. However, this way of tackling portfolio problems is not restricted to portfolio problems with default able assets only, but it provides a general framework allowing for a compact formulation of portfolio problems even if interest rates are stochastic.
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 criticizes the fact that profitability measures derived from capital market models such as the Sharpe ratio and the reward-to-VaR ratio are proposed for loan portfolios, although it is not proven whether their risk-return trade-offs are optimal for banks. The authors demonstrate that even the reward-to-VaR ratio, which is developed for valuating loan portfolios, can be highly misleading. They also show how market discipline, capital requirements, and insured deposits affect decision-making.
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.
Statistical analysis of stock markets and foreign exchange markets has demonstrated the intermittent nature of economic time series. A nonlinear model of business cycles is able to simulate intermittency arising from order-chaos and chaos-chaos transitions. This monograph introduces new concepts of unstable periodic orbits and chaotic saddles, which are unstable structures embedded in a chaotic attractor and responsible for economic intermittency.
This book revises the well-known capacity control problem in revenue management from the perspective of a risk-averse decision-maker. Modelling an expected utility maximizing decision maker, the problem is formulated as a risk-sensitive Markov decision process. Special emphasis is put on the existence of structured optimal policies. Numerical examples illustrate the results.
This volume features contributions to agent-based computational modeling from the social sciences and computer sciences. It presents applications of methodologies and tools, focusing on the uses, requirements, and constraints of agent-based models used by social scientists. Topics include agent-based macroeconomics, the emergence of norms and conventions, the dynamics of social and economic networks, and behavioral models in financial markets.
This book reconciles the existence of technical trading with the Efficient Market Hypothesis. By analyzing a well-known agent-based model, the Santa Fe Institute Artificial Stock Market (SFI-ASM), it finds that when selective forces are weak, financial evolution cannot guarantee that only the fittest trading rules will survive. Its main contribution lies in the application of standard results from population genetics which have widely been neglected in the agent-based community.
It has become part of the conventional wisdom in the economics of education that subsidies to higher education have a regressive distributional effect. Given that relatively more children from wealthier families enroll in higher education, many economist assume that these subsidies to higher education have an unwanted distributional impact. This volume presents new empirical evidence for the cross-sectional point of view and provides an analytical framework for the longitudinal perspective. The present volume also analyzes the equity and efficiency effects of widely-discussed funding reforms and proposes a voluntary graduate tax.
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.