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Straight after its invention in the early sixties, the Kalman filter approach became part of the astronautical guidance system of the Apollo project and therefore received immediate acceptance in the field of electrical engineer ing. This sounds similar to the well known success story of the Black-Scholes model in finance, which has been implemented by the Chicago Board of Op tions Exchange (CBOE) within a few month after its publication in 1973. Recently, the Kalman filter approach has been discovered as a comfortable estimation tool in continuous time finance, bringing together seemingly un related methods from different fields. Dr. B. Philipp Kellerhals contributes to this topic in several respects. Specialized versions of the Kalman filter are developed and implemented for three different continuous time pricing models: A pricing model for closed-end funds, taking advantage from the fact, that the net asset value is observable, a term structure model, where the market price of risk itself is a stochastic variable, and a model for electricity forwards, where the volatility of the price process is stochastic. Beside the fact that these three models can be treated independently, the book as a whole gives the interested reader a comprehensive account of the requirements and capabilities of the Kalman filter applied to finance models. While the first model uses a linear version of the filter, the second model using LIBOR and swap market data requires an extended Kalman filter. Finally, the third model leads to a non-linear transition equation of the filter algorithm.
Straight after its invention in the early sixties, the Kalman filter approach became part of the astronautical guidance system of the Apollo project and therefore received immediate acceptance in the field of electrical engineer ing. This sounds similar to the well known success story of the Black-Scholes model in finance, which has been implemented by the Chicago Board of Op tions Exchange (CBOE) within a few month after its publication in 1973. Recently, the Kalman filter approach has been discovered as a comfortable estimation tool in continuous time finance, bringing together seemingly un related methods from different fields. Dr. B. Philipp Kellerhals contributes to this topic in several respects. Specialized versions of the Kalman filter are developed and implemented for three different continuous time pricing models: A pricing model for closed-end funds, taking advantage from the fact, that the net asset value is observable, a term structure model, where the market price of risk itself is a stochastic variable, and a model for electricity forwards, where the volatility of the price process is stochastic. Beside the fact that these three models can be treated independently, the book as a whole gives the interested reader a comprehensive account of the requirements and capabilities of the Kalman filter applied to finance models. While the first model uses a linear version of the filter, the second model using LIBOR and swap market data requires an extended Kalman filter. Finally, the third model leads to a non-linear transition equation of the filter algorithm.
In this book, the authors investigate structural aspects of no arbitrage pricing of contingent claims and applications of the general pricing theory in the context of incomplete markets. A quasi-closed form pricing equation in terms of artificial probabilities is derived for arbitrary payoff structures. Moreover, a comparison between continuous and discrete models is presented, highlighting the major similarities and key differences. As applications, two sources of market incompleteness are considered, namely stochastic volatility and stochastic liquidity. Firstly, the general theory discussed before is applied to the pricing of power options in a stochastic volatility model. Secondly, the issue of liquidity risk is considered by focusing on the aspect of how asset price dynamics are affected by the trading strategy of a large investor.
Focuses on the analysis, optimization and controllability of time-discrete dynamical systems and games under the aspect of stability, controllability and (for games) cooperative and non-cooperative treatment. The investigation of stability is based on Lyapunov's method which is generalized to non-autonomous systems. Optimization and controllability of dynamical systems is treated, among others, with the aid of mapping theorems such as implicit function theorem and inverse mapping theorem. Dynamical games are treated as cooperative and non-cooperative games and are used in order to deal with the problem of carbon dioxide reduction under economic aspects. The theoretical results are demonstrated by various applications.
1. 1 Objective of the Study Vector autoregressive (VAR) models have become one of the dominant research tools in the analysis of macroeconomic time series during the last two decades. The great success of this modeling class started with Sims' (1980) critique of the traditional simultaneous equation models (SEM). Sims criticized the use of 'too many incredible restrictions' based on 'supposed a priori knowledge' in large scale macroeconometric models which were popular at that time. Therefore, he advo cated largely unrestricted reduced form multivariate time series models, unrestricted VAR models in particular. Ever since his influential paper these models have been employed extensively to characterize the underlying dynamics in systems of time series. In particular, tools to summarize the dynamic interaction between the system variables, such as impulse response analysis or forecast error variance decompo sitions, have been developed over the years. The econometrics of VAR models and related quantities is now well established and has found its way into various textbooks including inter alia Llitkepohl (1991), Hamilton (1994), Enders (1995), Hendry (1995) and Greene (2002). The unrestricted VAR model provides a general and very flexible framework that proved to be useful to summarize the data characteristics of economic time series. Unfortunately, the flexibility of these models causes severe problems: In an unrestricted VAR model, each variable is expressed as a linear function of lagged values of itself and all other variables in the system.
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.
This work uses various model frameworks to study the evolution of equilibria in an open loop evolving economy in which the model characteristics evolve without any directional restrictions except for continuity. Applying mathematical methods, it is shown that equilibria can always be adapted in a piecewise gradual, non bang-bang way.
Because of the clearly important role cooperative systems play in areas such as military sciences, biology, communications, robotics, and economics, just to name a few, the study of cooperative systems has intensified. This book provides an insight in the basic understanding of cooperative systems as well as in theory, modeling, and applications of cooperative control, optimization and related problems.
The book contains invited papers by well-known experts on a wide range of topics (economics, variational analysis, probability etc.) closely related to convexity and generalized convexity, and refereed contributions of specialists from the world on current research on generalized convexity and applications, in particular, to optimization, economics and operations research.
This book constitutes the refereed proceedings of the Second Theory of Cryptography Conference, TCC 2005, held in Cambridge, MA, USA in February 2005. The 32 revised full papers presented were carefully reviewed and selected from 84 submissions. The papers are organized in topical sections on hardness amplification and error correction, graphs and groups, simulation and secure computation, security of encryption, steganography and zero knowledge, secure computation, quantum cryptography and universal composability, cryptographic primitives and security, encryption and signatures, and information theoretic cryptography.