Copula Structure Analysis Based on Robust and Extreme Dependence Measures

In this paper we extend the standard approach of correlation structure analysis in order to reduce the dimension of highdimensional statistical data. The classical assumption of a linear model for the distribution of a random vector is replaced by the weaker assumption of a model for the copula. For elliptical copulae a correlation-like structure remains but different margins and non-existence of moments are possible. Moreover, elliptical copulae allow also for a copula structure analysis of dependence in extremes. After introducing the new concepts and deriving some theoretical results we observe in a simulation study the performance of the estimators: the theoretical asymptotic behavior of the statistics can be observed even for a sample of only 100 observations. Finally, we test our method on real financial data and explain differences between our copula based approach and the classical approach. Our new method yields a considerable dimension reduction also in non-linear models

Modelling, Estimation and Visualization of Multivariate Dependence for Risk Management

Dependence modelling and estimation is a key issue in the assessment of portfolio risk. When measuring extreme risk in terms of the Value-at-Risk, the multivariate normal model with linear correlation as its natural dependence measure is by no means an ideal model. We suggest a large class of models and a new dependence function which allows us to capture the complete extreme dependence structure of a portfolio. We also present a simple nonparametric estimation procedure. To show our new method at work we apply it to a financial data set of zero coupon swap rates and estimate the extreme dependence in the data

Estimating Tail Dependence of Elliptical Distributions

Recently there has been an increasing interest in applying elliptical distributions to risk management. Under weak conditions, Hult and Lindskog (2002) showed that a random vector with an elliptical distribution is in the domain of attraction of a multivariate extreme value distribution. In this paper we study two estimators for the tail dependence function, which are based on extreme value theory and the structure of an elliptical distribution, respectively. After deriving second order regular variation estimates and proving asymptotic normality for both estimators, we show that the estimator based on the structure of an elliptical distribution is better than that based on extreme value theory in terms of both asymptotic variance and optimal asymptotic mean squared error.Our theoretical results are confirmed by a simulation study

Dependence Estimation and Visualization in Multivariate Extremes with Applications to Financial Data

We investigate extreme dependence in a multivariate setting with special emphasis on financial applications. We introduce a new dependence function which allows us to capture the complete extreme dependence structure and present a nonparametric estimation procedure. The new dependence function is compared with existing measures including the spectral measure and other devices measuring extreme dependence. We also apply our method to a financial data set of zero coupon swap rates and estimate the extreme dependence in the data

Über Abhängigkeitsstrukturen und Extrema

This thesis deals with various aspects of multivariate dependencies and extreme values. First, a new dependence measure is developed and non-parametrical estimator as well as a concept of visualization of extremes. Also, tail-copula estimators are developed under the assumptions of having either elliptical distributions or elliptical copula. Of these, the asymptotic behavior of first and second order is determined and the improvements compared to non-parametric estimators are shown both theoretical and by simulation. Another chapter extends correlation structure analysis to copulae. Therefore, copula-based estimators are designed and their asymptotic behavior is shown, where a tail-copula estimator allows for a structure analysis of extremes. Finally, the extreme value distribution of a credit default portfolio is proven for a wide and flexible class of default distributions and an improved concept of fitting the portfolio-distribution is shown.Diese Dissertation behandelt unterschiedliche Aspekte multivariater Abhängigkeitsstrukturen und Extremwerte (EW). Es wird zunächst ein neues Abhängigkeitsmass und dafür ein nichtparametrischer Schätzer entwickelt sowie ein Konzept zur Visualisierung von EWn gezeigt. Ebenfalls werden Tailcopula (TC) Schätzer unter elliptischen Verteilungen und Copulae konstruiert, deren asymptotisches Verhalten 1. und 2. Ordnung gezeigt und theoretisch und mittels Simulation werden die Verbesserungen gegenüber dem nichtparametrischen Schätzer gezeigt. Ein weiterer Abschnitt erweitert die Korrelations-Struktur-Analyse auf Copulae. Dazu werden Copula-basierte Schätzer entwickelt sowie deren asymptotische Eigenschaften hergeleitet und ein TC-gestützter Schätzer erlaubt eine Strukturanalyse der EW. Zuletzt wird die Extremwertverteilung eines Credit-Default Portfolios für unterschiedliche Ausfallverteilungen bestimmt sowie ein verbessertes Verfahren zur Anpassung der Portfolioverteilung gezeigt

Library Scholarly Communication Initiatives at the University of North Dakota

Librarians at the University of North Dakota (UND) are implementing scholarly communication initiatives in partnership with faculty and other campus groups to bring about a greater awareness and understanding of related topics, including: open access, open educational resources, researcher IDs and communities, metrics and altmetrics, journal quality indicators, data management, copyright and author’s rights, and publishing strategies. At UND, there is a campus-wide effort for colleges to identify the top high quality journals in their fields or disciplines, and to track faculty scholarly publishing/research outputs for heightened research visibility and impact. The presenters share their experience engaging in these initiatives, as well as information on the broader environment surrounding scholarly communication activities on campus.https://commons.und.edu/cfl-lpp/1004/thumbnail.jp

Multivariate Tail Copula: Modeling and Estimation

In general, risk of an extreme outcome in financial markets can be expressed as a function of the tail copula of a high-dimensional vector after standardizing marginals. Hence it is of importance to model and estimate tail copulas. Even for moderate dimension, nonparametrically estimating a tail copula is very inefficient and fitting a parametric model to tail copulas is not robust. In this paper we propose a semi-parametric model for tail copulas via an elliptical copula. Based on this model assumption, we propose a novel estimator for the tail copula, which proves favourable compared to the empirical tail copula, both theoretically and empirically

Not Just a Trick: A survey study exploring how ‘exposing’ exhibition visitors to science of magic concepts impacts their appreciation of magic

The recent rise in scientific research on magic raises important issues about the impact that the dissemination of magic knowledge has on people’s appreciation of magic.Deception, secrecy, and mystery are inexorably intertwined with the idea of performance magic. Magicians traditionally do not reveal their secret methods to non-magicians. This study used a survey to assess how people’s appreciation of magic was impacted by a magic exhibition designed to highlight and reveal the psychological mechanisms that underpin magic. Visitors to the exhibition were asked to rate the impact of the exhibition on a range of measures assessing people’s interest and appreciation for magic. The results revealed significant positive impacts across multiple dimensions. We also conducted a qualitative analysis on people’s self-reports about things that they like and dislike about magic as well as the impact that scientific explanations have on people’s appreciation for magic. Despite magicians’ traditional fear that revelations related to magic secretes might rob magic audiences of their sense of wonder, our results indicate that an engaging exhibition about the science that underpins some magical experiences can actually enhance peoples’ stated appreciation of magic

The mod 2 homology of infinite loopspaces

We study the spectral sequence that one obtains by applying mod 2 homology to the Goodwillie tower which sends a spectrum X to the suspension spectrum of its 0th space X_0. This converges strongly to H_*(X_0) when X is 0-connected. The E^1 term is the homology of the extended powers of X, and thus is a well known functor of H_*(X), including structure as a bigraded Hopf algebra, a right module over the mod 2 Steenrod algebra A, and a left module over the Dyer-Lashof operations. Hopf algebra considerations show that all pages of the spectral sequence are primitively generated, with primitives equal to a subquotient of the primitives in E^1. We use an operad structure on the tower and the Z/2 Tate construction to show how Dyer-Lashof operations and differentials interact. These then determine differentials that hold for any spectrum X. These universal differentials then lead us to construct, for every A-module M, an algebraic spectral sequence depending functorially on M. The algebraic spectral sequence for H_*(X) agrees with the topological spectral sequence for X for many spectra, including suspension spectra and almost all generalized Eilenberg-MacLane spectra, and appears to give an upper bound in general. The E^infty term of the algebraic spectral sequence has form and structure similar to E^1, but now the right A-module structure is unstable. Our explicit formula involves the derived functors of destabilization as studied in the 1980's by W. Singer, J. Lannes and S. Zarati, and P. Goerss.Comment: 45 pages, latest version has reorganized examples, and makes better use of Hopf algebra methods. Now appeared in AGT 13 (2013

Projeto de um edifício hotel de 12 andares em concreto armado com a utilização do software TQS

Este trabalho consiste na elaboração do projeto estrutural de um edifício hotel de 12 pavimentos em concreto armado, desenvolvido a partir de plantas arquitetônicas em fase de estudo preliminar. O projeto é elaborado contemplando desde a etapa de concepção estrutural, que deve ser feita de maneira a respeitar o desenho projetivo proposto pela arquitetura e, ao mesmo tempo, garantir uma estrutura segura e confortável aos usuários, até a etapa de produção das pranchas de detalhamento, que devem ser feitas da forma mais clara e detalhada possível para garantir a correta execução na obra. O trabalho também contempla as etapas de lançamento, dimensionamento e verificação dos elementos estruturais de concreto armado. Para esta tarefa foi utilizado o software TQS, que é um programa especializado em projetos estruturais em concreto armado e é referência no mercado brasileiro pela sua eficiência e riqueza de recursos. Além da produção das plantas de detalhamento, outro objetivo do trabalho é a integração com plataforma BIM (Building Information Modeling) através da geração de um arquivo de modelo 3D da edificação