Modelling Correlations in Portfolio Credit Risk

The risk of a credit portfolio depends crucially on correlations between the probability of default (PD) in different economic sectors. Often, PD correlations have to be estimated from relatively short time series of default rates, and the resulting estimation error hinders the detection of a signal. We present statistical evidence that PD correlations are well described by a (one-)factorial model. We suggest a method of parameter estimation which avoids in a controlled way the underestimation of correlation risk. Empirical evidence is presented that, in the framework of the CreditRisk+ model with integrated correlations, this method leads to an increased reliability of the economic capital estimate.Comment: 5 pages, 4 figure

Unemployment in an Estimated New Keynesian Model

We reformulate the Smets-Wouters (2007) framework by embedding the theory of unemployment proposed in Galí (2011a,b). We estimate the resulting model using postwar U.S. data, while treating the unemployment rate as an additional observable variable. Our approach overcomes the lack of identification of wage markup and labor supply shocks highlighted by Chari, Kehoe and McGrattan (2008) in their criticism of New Keynesian models, and allows us to estimate a "correct" measure of the output gap. In addition, the estimated model can be used to analyze the sources of unemployment fluctuations.nominal rigidities, unemployment fluctuations, Phillips curve, wage markups shocks, output gap.

Unemployment in an estimated new Keynesian model

We reformulate the Smets-Wouters (2007) framework by embedding the theory of unemployment proposed in Galí (2011a,b). We estimate the resulting model using postwar U.S. data, while treating the unemployment rate as an additional observable variable. Our approach overcomes the lack of identification of wage markup and labor supply shocks highlighted by Chari, Kehoe and McGrattan (2008) in their criticism of New Keynesian models, and allows us to estimate a "correct" measure of the output gap. In addition, the estimated model can be used to analyze the sources of unemployment fluctuations.nominal rigidities, unemployment fluctuations, Phillips curve, wage markups shocks, output gap

The sharp constant in the Hardy-Sobolev-Maz'ya inequality in the three dimensional upper half-space

It is shown that the sharp constant in the Hardy-Sobolev-Maz'ya inequality on the three dimensional upper half space is given by the Sobolev constant. This is achieved by a duality argument relating the problem to a Hardy-Littlewood-Sobolev type inequality whose sharp constant is determined as well.Comment: 9 page

Ground state energy of large polaron systems

The last unsolved problem about the many-polaron system, in the Pekar-Tomasevich approximation, is the case of bosons with the electron-electron Coulomb repulsion of strength exactly 1 (the 'neutral case'). We prove that the ground state energy, for large $N$, goes exactly as $-N^{7/5}$, and we give upper and lower bounds on the asymptotic coefficient that agree to within a factor of $2^{2/5}$.Comment: 16 page

Algebraic Overshear Density Property

We introduce the notion of the algebraic overshear density property which implies both the algebraic notion of flexibility and the holomorphic notion of the density property. We investigate basic consequences of this stronger property, and propose further research directions in this borderland between affine algebraic geometry and elliptic holomorphic geometry.Comment: 13 page

Low-Fat Dairy Coffee Whitener

A coffee whitener composition made from decreamed milk ultrafiltration retentate having its protein concentrated between about 2:1 to about 4:1 compared to the protein content of the starting milk and a minor whitening power enhancing amount is added in the form of riboflavin (a vitamin) and beta carotene (a vitamin pre-cursor) or a mixture thereof. The composition is usually in powdered form and is high in protein, low in fat and sodium and reduced in lactose and its high protein enhanced as described provided a low-fat dairy coffee whitening function approximately equal to non-diary coffee creamers

OpenML Benchmarking Suites

Machine learning research depends on objectively interpretable, comparable, and reproducible algorithm benchmarks. Therefore, we advocate the use of curated, comprehensive suites of machine learning tasks to standardize the setup, execution, and reporting of benchmarks. We enable this through software tools that help to create and leverage these benchmarking suites. These are seamlessly integrated into the OpenML platform, and accessible through interfaces in Python, Java, and R. OpenML benchmarking suites are (a) easy to use through standardized data formats, APIs, and client libraries; (b) machine-readable, with extensive meta-information on the included datasets; and (c) allow benchmarks to be shared and reused in future studies. We also present a first, carefully curated and practical benchmarking suite for classification: the OpenML Curated Classification benchmarking suite 2018 (OpenML-CC18)