The use of Monte Carlo techniques for the optimization of stochastic control systems

Imperial Users onl

Artin's primitive root conjecture -a survey -

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

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

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

Robust estimation for the mean of skewed distributions

Common estimators of the mean g(θ) = Jx dFθ(x) in skewed distribution models may be sensitive to contamination by a few large observations. It is then desirable to consider robust estimators g(θ) .The approach of Hampel (1968), who defines an estimator θ for the parameter vector θ to be optimal B-robust if it is asymptotically efficient subject to a given upper bound on the norm of its influence function, is used to construct optimal robust estimators for g(θ) . An estimator g(θ) is defined to be functional invariant when it preserves the robustness and optimality properties of a robust estimator θ . The invariance of the optimal B-robust estimators are used to construct optimal B-robust estimator for the mean of multi-parameter distributions. An algorithm for computing the optimal B-robust score function for any distribution is developed. An optimal B-robust L-estimator for the location-scale family is also constructed. Asymptotic relative efficiencies of the optimal B-robust estimators for the mean of the lognormal and Weibull distributions are computed and compared with those for several other robust and nonrobust estimators. Type II censoring is considered as a method to achieve B-robustness. The optimal proportion of trimming is defined as that proportion which produces the smallest asymptotic MSE in the class of censored data estimators subject to some upper bound on the influence function. Several common estimators for censored data, including the maximum likelihood, a modified maximum likelihood [Tiku et al., 1986] and an L-estimator [Chernoff, et al. ,1967], are shown to have larger MSE than the optimal B-robust estimator with the same upper bound on the influence function. The optimal proportions of trimming are computed for the MLE and L-estimator of the mean of lognormal and Weibull distributions. A simulation study of nine estimators for the mean of a lognormal distribution shows that the optimal B-robust estimator has the smallest MSE for the sample size and contamination cases considered. All B-robust estimators considered are found to be better than the nonrobust ones with regard to both MSE and bias