Avoiding the rating bounce : why rating agencies are slow to react to new information

Rating agencies state that they take a rating action only when it is unlikely to be reversed shortly afterwards. Based on a formal representation of the rating process, I show that such a policy provides a good explanation for the empirical evidence: Rating changes occur relatively seldom, exhibit serial dependence, and lag changes in the issuers’ default risk. In terms of informational losses, avoiding rating reversals can be more harmful than monitoring credit quality only twice per year

Wald Statistics in high-dimensional PCA

In this note we consider PCA for Gaussian observations $X_1,\dots, X_n$ with covariance $\Sigma=\sum_i \lambda_i P_i$ in the 'effective rank' setting with model complexity governed by $\mathbf{r}(\Sigma):=\text{tr}(\Sigma)/\| \Sigma \|$. We prove a Berry-Essen type bound for a Wald Statistic of the spectral projector $\hat P_r$. This can be used to construct non-asymptotic confidence ellipsoids and tests for spectral projectors $P_r$. Using higher order pertubation theory we are able to show that our Theorem remains valid even when $\mathbf{r}(\Sigma) \gg \sqrt{n}$.Comment: 11 page

Two Kinds of ’Christian Philosophy’

It is controversial whether ”Christian Philosophy’ is a useful or even consistent notion. After providing some historical background to the problem, I will distinguish and explicate two possible understandings of ”Christian Philosophy’ which should be kept apart: a ”Thomistic’ and an ”Augustinian’ one, of which the latter has garnered more attention in the recent literature. A sketch of the most prominent current ”Augustinian’ position leads to some considerations for why a ”Thomistic’ understanding of ”Christian Philosophy’ has more to recommend it, if the term is regarded as useful at all

Electron vortices in crystals

The propagation of electron beams carrying angular momentum in crystals is studied using a multislice approach for the model system Fe. It is found that the vortex beam is distorted strongly due to elastic scattering. Consequently, the expectation value of the angular momentum as well as the local vortex components change with the initial position of the vortex and the propagation depth, making numerical simulations indispensable when analyzing experiments

A rigorous but gentle introduction for economists

This open access textbook is the first to provide Business and Economics Ph.D. students with a precise and intuitive introduction to the formal backgrounds of modern financial theory. It explains Brownian motion, random processes, measures, and Lebesgue integrals intuitively, but without sacrificing the necessary mathematical formalism, making them accessible for readers with little or no previous knowledge of the field. It also includes mathematical definitions and the hidden stories behind the terms discussing why the theories are presented in specific ways.

Unions of Onions: Preprocessing Imprecise Points for Fast Onion Decomposition

Let $\mathcal{D}$ be a set of $n$ pairwise disjoint unit disks in the plane. We describe how to build a data structure for $\mathcal{D}$ so that for any point set $P$ containing exactly one point from each disk, we can quickly find the onion decomposition (convex layers) of $P$. Our data structure can be built in $O(n \log n)$ time and has linear size. Given $P$, we can find its onion decomposition in $O(n \log k)$ time, where $k$ is the number of layers. We also provide a matching lower bound. Our solution is based on a recursive space decomposition, combined with a fast algorithm to compute the union of two disjoint onionComment: 10 pages, 5 figures; a preliminary version appeared at WADS 201