51 research outputs found

    Identification of physical models

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    Artin's primitive root conjecture -a survey -

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    This is an expanded version of a write-up of a talk given in the fall of 2000 in Oberwolfach. A large part of it is intended to be understandable by non-number theorists with a mathematical background. The talk covered some of the history, results and ideas connected with Artin's celebrated primitive root conjecture dating from 1927. In the update several new results established after 2000 are also discussed.Comment: 87 pages, 512 references, to appear in Integer

    The 1981 NASA/ASEE Summer Faculty Fellowship Program: Research reports

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    Research reports related to spacecraft industry technological advances, requirements, and applications were considered. Some of the topic areas addressed were: (1) Fabrication, evaluation, and use of high performance composites and ceramics, (2) antenna designs, (3) electronics and microcomputer applications and mathematical modeling and programming techniques, (4) design, fabrication, and failure detection methods for structural materials, components, and total systems, and (5) chemical studies of bindary organic mixtures and polymer synthesis. Space environment parameters were also discussed

    An Integrated System for Market Risk, Credit Risk and Portfolio Optimization Based on Heavy-Tailed Medols and Downside Risk Measures

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    Gängige Theorien der mathematischen Finanzwirtschaft wie zum Beispiel der Mean-Variance-Ansatz zur Portfolio-Selektion oder Modelle zur Bewertung von Wertpapieren basieren alle auf der Annahme, dass Renditen im Zeitablauf unabhngig und identisch verteilt sind und einer Normalverteilung folgen. Empirische Untersuchungen liefern jedoch signifikante Hinweise dahingehend, dass diese Annahme f¨ur wichtige Anlageklassen unzutreffend ist. Stattdessen sindWertpapierrenditen zeitabh¨angige Volatilit¨aten, Heavy Tails (schwere Verteilungsr¨ander), Tail Dependence (Extremwertabh¨angigkeit) sowie Schiefe gekennzeichnet. Diese Eigenschaften haben Auswirkungen sowohl auf die theoretische als auch praktischeModellierung in der Finanzwirtschaft. Nach der Pr¨asentation des theoretischen Hintergrundes spricht die Arbeit die Modellierungsprobleme an, die sich aus diesen h¨aufig beobachteten Ph¨anomenen ergeben. Speziell werden Fragen bez¨uglich der Modellierung von Marktund Kreditrisiken volatiler M¨arkte behandelt als auch Probleme bei der Portfolio-Optimierung unter Verwendung alternativer Risikomae und Zielfunktionen. Fragen der praktischen Implementierung wird dabei besondere Aufmerksamkeit gewidmet.The cornerstone theories in finance, such as mean-variance model for portfolio selection and asset pricing models, that have been developed rest upon the assumption that asset returns follow an iid Gaussian distribution. There is, however, strong empirical evidence that this the assumption does not hold for most relevant asset classes. Financial return series typically exhibit volatility clustering, heavy-tailedness, tail dependence, and skewness. These properties have implications for both theoretical and practical modeling in finance. After providing some theoretical background, this thesis addresses modeling issues arising from these commonly observed phenomena. Specifically, questions pertaining assessing and modeling market- and credit-risk in volatile markets and portfolio-optimization problems under use of alternative risk measures and objective functions are investigated. Practical implementation is a concern throughout the analysis
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