On Liability Insurance for Automobiles

Car owners are liable for property damage inflicted on other motorists. In most countries such liability must be insured by law. That law may favor expensive or heavy vehicles, prone to suffer or inflict large losses. This paper explores links between liability rules and vehicle choice. It presumes cooperative insurance, but non-cooperative acquisition of vehicles. Thus, the Nash equilibrium and its degree of efficiency depend on the liability regime

A martingale-transform goodness-of-fit test for the form of the conditional variance

In the common nonparametric regression model the problem of testing for a specific parametric form of the variance function is considered. Recently Dette and Hetzler (2008) proposed a test statistic, which is based on an empirical process of pseudo residuals. The process converges weakly to a Gaussian process with a complicated covariance kernel depending on the data generating process. In the present paper we consider a standardized version of this process and propose a martingale transform to obtain asymptotically distribution free tests for the corresponding Kolmogorov-Smirnov and Cram\'{e}r-von-Mises functionals. The finite sample properties of the proposed tests are investigated by means of a simulation study.Comment: 24 pages

Some asymptotic properties of the spectrum of the Jacobi ensemble

For the random eigenvalues with density corresponding to the Jacobi ensemble $$c \cdot \prod_{i < j} | \lambda_i - \lambda_j |^\beta \prod^n_{i=1} (2 - \lambda_i)^a (2 + \lambda_i)^b I_{(-2,2)} (\lambda_i)$$ $(a, b > -1, \beta > 0)$ a strong uniform approximation by the roots of the Jacobi polynomials is derived if the parameters $a, b,$ $\beta$ depend on $n$ and $n \to \infty$. Roughly speaking, the eigenvalues can be uniformly approximated by roots of Jacobi polynomials with parameters $((2a+2)/\beta -1, (2b+2)/\beta-1)$, where the error is of order $\{\log n/(a+b) \}^{1/4}$. These results are used to investigate the asymptotic properties of the corresponding spectral distribution if $n \to \infty$ and the parameters $a, b$ and $\beta$ vary with $n$. We also discuss further applications in the context of multivariate random $F$-matrices.Comment: 20 pages, 2 figure

Moderate deviations for the eigenvalue counting function of Wigner matrices

We establish a moderate deviation principle (MDP) for the number of eigenvalues of a Wigner matrix in an interval. The proof relies on fine asymptotics of the variance of the eigenvalue counting function of GUE matrices due to Gustavsson. The extension to large families of Wigner matrices is based on the Tao and Vu Four Moment Theorem and applies localization results by Erd\"os, Yau and Yin. Moreover we investigate families of covariance matrices as well.Comment: 20 page

Three approaches towards Floer homology of cotangent bundles

Consider the cotangent bundle of a closed Riemannian manifold and an almost complex structure close to the one induced by the Riemannian metric. For Hamiltonians which grow for instance quadratically in the fibers outside of a compact set, one can define Floer homology and show that it is naturally isomorphic to singular homology of the free loop space. We review the three isomorphisms constructed by Viterbo (1996), Salamon-Weber (2003) and Abbondandolo-Schwarz (2004). The theory is illustrated by calculating Morse and Floer homology in case of the euclidean n-torus. Applications include existence of noncontractible periodic orbits of compactly supported Hamiltonians on open unit disc cotangent bundles which are sufficiently large over the zero section.Comment: 30 pages, 6 figures. To appear in J. Symplectic Geom. (Stare Jablonki conference issue

Diversity-Konzept 2011–2014 der Goethe-Universität Frankfurt am Main

The “Diversity Concept of the Goethe University Frankfurt am Main 2011–2014” is based on the goals as laid down in the University Development Plan 2011. The Goethe University combined various instruments for working out the concept, not least in order to ensure adequate participation: on the one hand, guided interviews were conducted, for example, with employees in advisory functions, members of the AStA (General Students’ Commit-tee), etc. On the other hand, Internet research, an open space workshop, as well as four strategy and awareness-raising workshops on various topics were organized. The concept was developed in close cooperation with the vice president responsible for gender and diversity, Prof. Dr. Roser Valenti, the Senate Commission “Advancement of Women, Equal Opportunity, and Diversity”, the “Project Supervision Group Diversity Poli-cies”, and the Equal Opportunities Office. The Goethe University already has various concepts and target agreements on gender equal-ity and family support. The Diversity Concept therefore includes no measures on these top-ics. With the expiry of the Plan for the Advancement of Women in 2014, all of the other reports and measures related to equal opportunity and diversity will be consolidated in a central “Gender Equality & Diversity Action Plan of the Goethe University Frankfurt am Main” (GEDAP) and updated every four years.Das »Diversity-Konzept der Goethe-Universität Frankfurt am Main 2011 – 2014« basiert auf den im Hochschulentwicklungsplan 2011 festgelegten Zielen der Universität. Für die Erarbeitung des Konzeptes hat die Goethe-Universität verschiedene Instrumente kombiniert, nicht zuletzt, um eine ausreichende Partizipation zu gewährleisten: So wurden zum einen Leitfadeninterviews mit Beschäftigten in Beratungsfunktionen, Mitgliedern des AStA und anderen geführt. Zum anderen wurden eine Internetrecherche, ein Open-Space-Workshop sowie vier Strategie- und Sensibilisierungs-Workshops mit unterschiedlichen Themenstellungen organisiert. Das Konzept entstand in enger Zusammenarbeit zwischen der für Gleichstellung zuständigen Vizepräsidentin, Prof. Roser Valenti, der Senatskommission »Frauenförderung, Gleichstellung und Diversität«, der »Projektsteuerungsgruppe diversityPolicies« und dem Gleichstellungsbüro. An der Goethe-Universität liegen bereits verschiedene Konzepte und Zielvereinbarungen zur Geschlechtergleichstellung und Familienförderung vor. Das Diversity-Konzept sieht deshalb dazu keine Maßnahmen vor. Mit Auslaufen des Frauenförderplans im Jahr 2014 werden gleichstellungs- und andere diversitätsbezogene Berichte und Maßnahmen in einem zentralen »Gender Equality & Diversity Action Plan« (GEDAP) der Goethe-Universität Frankfurt am Main zusammengefasst und alle vier Jahre fortgeschrieben