### Refine

#### Year of publication

- 2001 (7) (remove)

#### Language

- English (7) (remove)

#### Has Fulltext

- yes (7) (remove)

#### Keywords

- n.a. (2)
- Abfrageverarbeitung (1)
- Approximation (1)
- Arbitrage-Pricing-Theorie (1)
- Client-server-Konzept (1)
- Derivat <Wertpapier> (1)
- Diversifikation (1)
- Euro <Währung> (1)
- Fallbasiertes Schließen (1)
- Foreign Exchange Reserves (1)
- Grundwasserstrom (1)
- Hadamard product (1)
- Hyperlink-Proposals (1)
- Internetdienst (1)
- Konfluente hypergeometrische Funktion (1)
- Kontrolltheorie (1)
- Konvexe Optimierung (1)
- Methode der logarithmischen Barriere (1)
- Navier-Stokes equations (1)
- Navier-Stokes-Gleichung (1)
- Nebenbedingung (1)
- Numerisches Verfahren (1)
- Optimale Kontrolle (1)
- Orthogonale Zerlegung (1)
- Partielle Differentialgleichung (1)
- Regularisierung (1)
- Request-Prediction (1)
- Semiinfinite Optimierung (1)
- Sequentielle quadratische Optimierung (1)
- Strömungsmechanik (1)
- Taiwan (1)
- Transaktionskosten (1)
- Trust-Region-Algorithmus (1)
- Web-Applications (1)
- Währungsreserve (1)
- confluent hypergeometric function (1)
- eigenfunction expansion (1)
- financial derivatives (1)
- flow control (1)
- pricing (1)
- proper orthogonal decomposition (1)
- reduced order modelling (1)
- series expansion (1)
- transaction costs (1)
- trust-region method (1)

#### Institute

- Mathematik (5)
- Informatik (1)
- Wirtschaftswissenschaften (1)

This work is concerned with the numerical solution of optimization problems that arise in the context of ground water modeling. Both ground water hydraulic and quality management problems are considered. The considered problems are discretized problems of optimal control that are governed by discretized partial differential equations. Aspects of special interest in this work are inaccurate function evaluations and the ensuing numerical treatment within an optimization algorithm. Methods for noisy functions are appropriate for the considered practical application. Also, block preconditioners are constructed and analyzed that exploit the structure of the underlying linear system. Specifically, KKT systems are considered, and the preconditioners are tested for use within Krylov subspace methods. The project was financed by the foundation Stiftung Rheinland-Pfalz für Innovation and carried out in joint work with TGU GmbH, a company of consulting engineers for ground water and water resources.

Due to the breath-taking growth of the World Wide Web (WWW), the need for fast and efficient web applications becomes more and more urgent. In this doctoral thesis, the emphasis will be on two concrete tasks for improving Internet applications. On the one hand, a major problem of many of today's Internet applications may be described as the performance of the Client/Server-communication: servers often take a long time to respond to a client's request. There are several strategies to overcome this problem of high user-perceived latencies; one of them is to predict future user-requests. This way, time-consuming calculations on the server's side can be performed even before the corresponding request is being made. Furthermore, in certain situations, also the pre-fetching or the pre-sending of data might be appropriate. Those ideas will be discussed in detail in the second part of this work. On the other hand, a focus will be placed on the problem of proposing hyperlinks to improve the quality of rapid written texts, at first glance, an entirely different problem to predicting client requests. Ultra-modern online authoring systems that provide possibilities to check link-consistencies and administrate link management should also propose links in order to improve the usefulness of the produced HTML-documents. In the third part of this elaboration, we will describe a possibility to build a hyperlink-proposal module based on statistical information retrieval from hypertexts. These two problem categories do not seem to have much in common. It is one aim of this work to show that there are certain, similar solution strategies to look after both problems. A closer comparison and an abstraction of both methodologies will lead to interesting synergetic effects. For example, advanced strategies to foresee future user-requests by modeling time and document aging can be used to improve the quality of hyperlink-proposals too.

The main purpose of this dissertation is to solve the following question: How will the emergence of the Euro influence the currency composition of the NICs?monetary reserves? Taiwan and Thailand are chosen as our investigation subjects. There are two sorts of motives for central banks' reserve holdings, i.e., intervention-related motives and portfolio-related motives. The need for reserve holdings resulting from intervention-related motives are justified because of the costs resulting from exchange rate instability. On the other hand, we use the Tobin--Markowitz model to justify the need for monetary reserves held for portfolio-related motives. The operational implication of this distinction is the separation of monetary reserves into two tranches corresponding to different objectives. An analysis of a central bank's transaction balance is a money quality analysis. Such an analysis has to do with transaction costs and non-pecuniary rates of return. The facts point out, that the Euro's emergence will not change the fact that the USD will continue to be the major currency of transaction balances of the central banks in Taiwan and Thailand. In order to answer the question about diversification of monetary reserves as idle balance in the two NICs, we carry out an analysis of the portfolio approach, which is based on the basic ideas of the Tobin-Markowitz model. This analysis shows that Taiwan and/or Thailand respectively cannot reduce risk at a given rate of return or increase the rate of return at a given risk by diversifying their monetary reserves as idle balance from the USD to the Euro.

The discretization of optimal control problems governed by partial differential equations typically leads to large-scale optimization problems. We consider flow control involving the time-dependent Navier-Stokes equations as state equation which is stamped by exactly this property. In order to avoid the difficulties of dealing with large-scale (discretized) state equations during the optimization process, a reduction of the number of state variables can be achieved by employing a reduced order modelling technique. Using the snapshot proper orthogonal decomposition method, one obtains a low-dimensional model for the computation of an approximate solution to the state equation. In fact, often a small number of POD basis functions suffices to obtain a satisfactory level of accuracy in the reduced order solution. However, the small number of degrees of freedom in a POD based reduced order model also constitutes its main weakness for optimal control purposes. Since a single reduced order model is based on the solution of the Navier-Stokes equations for a specified control, it might be an inadequate model when the control (and consequently also the actual corresponding flow behaviour) is altered, implying that the range of validity of a reduced order model, in general, is limited. Thus, it is likely to meet unreliable reduced order solutions during a control problem solution based on one single reduced order model. In order to get out of this dilemma, we propose to use a trust-region proper orthogonal decomposition (TRPOD) approach. By embedding the POD based reduced order modelling technique into a trust-region framework with general model functions, we obtain a mechanism for updating the reduced order models during the optimization process, enabling the reduced order models to represent the flow dynamics as altered by the control. In fact, a rigorous convergence theory for the TRPOD method is obtained which justifies this procedure also from a theoretical point of view. Benefiting from the trust-region philosophy, the TRPOD method guarantees to save a lot of computational work during the control problem solution, since the original state equation only has to be solved if we intend to update our model function in the trust-region framework. The optimization process itself is completely based on reduced order information only.

This work is concerned with arbitrage bounds for prices of contingent claims under transaction costs, but regardless of other conceivable market frictions. Assumptions on the underlying market are held as weak as convenient for the deduction of meaningful results that make good economic sense. In discrete time we also allow for underlying price processes with uncountable state space. In continuous time the underlying price process is modeled by a semimartingale. For the most part we could avoid any stronger assumptions. The main problems with which we deal in this work are the modelling of (proportional) transaction costs, Fundamental Theorems of Asset Pricing under transaction costs, dual characterizations of arbitrage bounds under transaction costs, Quantile-Hedging under transaction costs, alternatives to the Black-Scholes model in continuous time (under transaction costs). The results apply to stock and currency markets.

In this thesis we focus on the development and investigation of methods for the computation of confluent hypergeometric functions. We point out the relations between these functions and parabolic boundary value problems and demonstrate applications to models of heat transfer and fluid dynamics. For the computation of confluent hypergeometric functions on compact (real or complex) intervals we consider a series expansion based on the Hadamard product of power series. It turnes out that the partial sums of this expansion are easily computable and provide a better rate of convergence in comparison to the partial sums of the Taylor series. Regarding the computational accuracy the problem of cancellation errors is reduced considerably. Another important tool for the computation of confluent hypergeometric functions are recurrence formulae. Although easy to implement, such recurrence relations are numerically unstable e.g. due to rounding errors. In order to circumvent these problems a method for computing recurrence relations in backward direction is applied. Furthermore, asymptotic expansions for large arguments in modulus are considered. From the numerical point of view the determination of the number of terms used for the approximation is a crucial point. As an application we consider initial-boundary value problems with partial differential equations of parabolic type, where we use the method of eigenfunction expansion in order to determine an explicit form of the solution. In this case the arising eigenfunctions depend directly on the geometry of the considered domain. For certain domains with some special geometry the eigenfunctions are of confluent hypergeometric type. Both a conductive heat transfer model and an application in fluid dynamics is considered. Finally, the application of several heat transfer models to certain sterilization processes in food industry is discussed.

The goal of this thesis is to transfer the logarithmic barrier approach, which led to very efficient interior-point methods for convex optimization problems in recent years, to convex semi-infinite programming problems. Based on a reformulation of the constraints into a nondifferentiable form this can be directly done for convex semi- infinite programming problems with nonempty compact sets of optimal solutions. But, by means of an involved max-term this reformulation leads to nondifferentiable barrier problems which can be solved with an extension of a bundle method of Kiwiel. This extension allows to deal with inexact objective values and subgradient information which occur due to the inexact evaluation of the maxima. Nevertheless we are able to prove similar convergence results as for the logarithmic barrier approach in the finite optimization. In the further course of the thesis the logarithmic barrier approach is coupled with the proximal point regularization technique in order to solve ill-posed convex semi-infinite programming problems too. Moreover this coupled algorithm generates sequences converging to an optimal solution of the given semi-infinite problem whereas the pure logarithmic barrier only produces sequences whose accumulation points are such optimal solutions. If there are certain additional conditions fulfilled we are further able to prove convergence rate results up to linear convergence of the iterates. Finally, besides hints for the implementation of the methods we present numerous numerical results for model examples as well as applications in finance and digital filter design.