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This thesis deals with the application of binomial option pricing in a single-asset Black-Scholes market and its extension to multi-dimensional situations. Although the binomial approach is, in principle, an efficient method for lower dimensional valuation problems, there are at least two main problems regarding its application: Firstly, traded options often exhibit discontinuities, so that the Berry- Esséen inequality is in general tight; i.e. conventional tree methods converge no faster than with order 1/sqrt(N). Furthermore, they suffer from an irregular convergence behaviour that impedes the possibility to achieve a higher order of convergence via extrapolation methods. Secondly, in multi-asset markets conventional tree construction methods cannot ensure well-defined transition probabilities for arbitrary correlation structures between the assets. As a major aim of this thesis, we present two approaches to get binomial trees into shape in order to overcome the main problems in applications; the optimal drift model for the valuation of single-asset options and the decoupling approach to multi-dimensional option pricing. The new valuation methods are embedded into a self-contained survey of binomial option pricing, which focuses on the convergence behaviour of binomial trees. The optimal drift model is a new one-dimensional binomial scheme that can lead to convergence of order o(1/N) by exploiting the specific structure of the valuation problem under consideration. As a consequence, it has the potential to outperform benchmark algorithms. The decoupling approach is presented as a universal construction method for multi-dimensional trees. The corresponding trees are well-defined for an arbitrary correlation structure of the underlying assets. In addition, they yield a more regular convergence behaviour. In fact, the sawtooth effect can even vanish completely, so that extrapolation can be applied.
Las matemáticas son atribuidas en general a algo no claro y sólo para matemáticos. La imagen de las matemáticas para los escolares, es la de una ciencia, la cual se sirve sólo de si misma. Es importante hacer frente al prejuicio de que las matemáticas distan lejos de toda utilidad práctica. La matemática es una ciencia al servicio de todas las dem´as ciencias, de cuya ayuda se necesita en casi todos los campos de la vida. La matemática de la escuela debería despertar en cualquier ámbito de la vida de los escolares el interés sobre ...
Linear Optimization is an important area from applied mathematics. A lot of practical problems can be modelled and solved with this technique. This publication shall help to introduce this topic to pupils. The process of modelling, the reduction of problems to their significant attributes shall be described. The linear programms will be solved by using the simplex method. Many examples illustrate the topic.
Lineare Optimierung ist ein wichtiges Aufgabengebiet der angewandten Mathematik, da sich viele praktische Probleme mittels dieser Technik modellieren und lösen lassen. Diese Veröffentlichung soll helfen, Schüler an diese Thematik heranzuführen. Dabei soll der Vorgang des Modellierens, also die Reduktion des Problems auf die wesentlichen Merkmale, vermittelt werden. Anschließend an den Modellierungsprozeß können durch Einsatz der Simplex-Methode die linearen Optimierungsprobleme gelöst werden. Verschiedene praktische Beispiele dienen der Veranschaulichung des Vorgehens.
Cellular membranes can serve as barriers between subcellular compartments, but they can also interact to form dynamically regulated membrane contact sites between a specific pair of organelles. Focussing on plants, this article discusses local redox environments and the current knowledge on membrane contact sites as examples for the dividing and connecting functions of membranes, respectively.
This publication tries to develop mathematical subjects for school from realistic problems. The center of this report are business planning and decision problems which occur in almost all companies. The main topics are: Calculation of raw material demand for given orders, consumption of existing stock and the lot sizing.
A mediados del año 1997 la publicación de los denominados TIMMS-Estudios (Third International Mathematics and Science Study) causó un importante impacto en el público alemán. El motivo de esto fue el rendimiento escolar conseguido en la rama de matemáticas y ciencias naturales del octavo curso, el cual estaba situado en un campo internacional, donde particularmente en el ámbito matemático el conjunto de los estados del norte-, oeste-, y del este de Europa que forman parte del TIMSS - sin mencionar a la mayoría de los paises asiáticos - habían conseguido claramente mejores rendimiento. En definitiva mostraban un peor rendimiento los escolares alemanes con respecto a los paises vecinos y con los ....
Mit der vorliegenden Veröffentlichung soll der Versuch unternommen werden, mathematischen Schulstoff aus konkreten Problemen herzuentwickeln. Im Mittelpunkt der vorliegenden Arbeit stehen betriebswirtschaftliche Planungs- und Entscheidungsprobleme, wie sie von fast allen Wirtschaftsunternehmen zu lösen sind. Dabei wird im besonderen auf folgende Optimierungsprobleme eingegangen: Berechnung des Rohstoffbedarfs bei gegebenen Bestellungen, Aufarbeitung von vorhandenen Lagerbeständen und das Stücklistenproblem.