Explicit solution of an inverse first-passage time problem for L\'{e}vy processes and counterparty credit risk

For a given Markov process $X$ and survival function $\overline{H}$ on $\mathbb{R}^+$, the inverse first-passage time problem (IFPT) is to find a barrier function $b:\mathbb{R}^+\to[-\infty,+\infty]$ such that the survival function of the first-passage time $\tau_b=\inf \{t\ge0:X(t)<b(t)\}$ is given by $\overline{H}$. In this paper, we consider a version of the IFPT problem where the barrier is fixed at zero and the problem is to find an initial distribution $\mu$ and a time-change $I$ such that for the time-changed process $X\circ I$ the IFPT problem is solved by a constant barrier at the level zero. For any L\'{e}vy process $X$ satisfying an exponential moment condition, we derive the solution of this problem in terms of $\lambda$-invariant distributions of the process $X$ killed at the epoch of first entrance into the negative half-axis. We provide an explicit characterization of such distributions, which is a result of independent interest. For a given multi-variate survival function $\overline{H}$ of generalized frailty type, we construct subsequently an explicit solution to the corresponding IFPT with the barrier level fixed at zero. We apply these results to the valuation of financial contracts that are subject to counterparty credit risk.Comment: Published at http://dx.doi.org/10.1214/14-AAP1051 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

Inference on the tail process with application to financial time series modelling

To draw inference on serial extremal dependence within heavy-tailed Markov chains, Drees, Segers and Warcho{\l} [Extremes (2015) 18, 369--402] proposed nonparametric estimators of the spectral tail process. The methodology can be extended to the more general setting of a stationary, regularly varying time series. The large-sample distribution of the estimators is derived via empirical process theory for cluster functionals. The finite-sample performance of these estimators is evaluated via Monte Carlo simulations. Moreover, two different bootstrap schemes are employed which yield confidence intervals for the pre-asymptotic spectral tail process: the stationary bootstrap and the multiplier block bootstrap. The estimators are applied to stock price data to study the persistence of positive and negative shocks.Comment: 22 page

Streaming velocities as a dynamical estimator of Omega

It is well known that estimating the pairwise velocity of galaxies, v_{12}, from the redshift space galaxy correlation function is difficult because this method is highly sensitive to the assumed model of the pairwise velocity dispersion. Here we propose an alternative method to estimate v_{12} directly from peculiar velocity samples, which contain redshift-independent distances as well as galaxy redshifts. In contrast to other dynamical measures which determine beta = sigma_8 x Omega^{0.6}, our method can provide an estimate of (sigma_8)^2 x Omega^{0.6} for a range of sigma_8 (here Omega is the cosmological mass density parameter while sigma_8 is the standard normalization parameter for the spectrum of matter density fluctuations). We demonstrate how to measure this quantity from realistic catalogues.Comment: 8 pages of text, 4 figures Subject headings: Cosmology: theory - observation - peculiar velocities: large scale flows Last name of one of the authors was misspelled. It is now corrected. Otherwise the manuscript is identical to its original versio

Evidence for a low-density Universe from the relative velocities of galaxies

The motions of galaxies can be used to constrain the cosmological density parameter Omega and the clustering amplitude of matter on large scales. The mean relative velocity of galaxy pairs, estimated from the Mark III survey, indicates that Omega = 0.35 +0.35/-0.25. If the clustering of galaxies is unbiased on large scales, Omega = 0.35 +/- 0.15, so that an unbiased Einstein-de Sitter model (Omega = 1) is inconsistent with the data.Comment: 12 pages, 2 figures, to appear in the Jan.7 issue of ``Science''; In the original version, the title appeared twice. This problem has now been corrected. No other changes were mad

Measuring Omega with Galaxy Streaming Velocities

The mean pairwise velocity of galaxies has traditionally been estimated from the redshift space galaxy correlation function. This method is notorious for being highly sensitive to the assumed model of the pairwise velocity dispersion. Here we propose an alternative method to estimate the streaming velocity directly from peculiar velocity samples, which contain redshift-independent distances as well as galaxy redshifts. This method can provide an estimate of $\Omega^{0.6}\sigma_8^2$ for a range of $\sigma_8$ where $\Omega$ is the cosmological density parameter, while $\sigma_8$ is the standard normalization for the power spectrum of density fluctuations. We demonstrate how to measure this quantity from realistic catalogues and identify the main sources of bias and errorsComment: Proceedings of New Worlds in Astroparticle Physics, 6 pages, 2 figure

Determination of the gaseous hydrogen ductile-brittle transition in copper-nickel alloys

A series of copper-nickel alloys were fabricated, notched tensile specimens machined for each alloy, and the specimens tested in 34.5 MPa hydrogen and in air. A notched tensile ratio was determined for each alloy and the hydrogen environment embrittlement (HEE) determined for the alloys of 47.7 weight percent nickel to 73.5 weight percent nickel. Stacking fault probability and stacking fault energies were determined for each alloy using the x ray diffraction line shift and line profiles technique. Hydrogen environment embrittlement was determined to be influenced by stacking fault energies; however, the correlation is believed to be indirect and only partially responsible for the HEE behavior of these alloys

Cosmic-Ray Spectra in Interstellar Space

At energies below ~300 MeV/nuc our knowledge of cosmic-ray spectra outside the heliosphere is obscured by the energy loss that cosmic rays experience during transport through the heliosphere into the inner solar system. This paper compares measurements of secondary electron-capture isotope abundances and cosmic-ray spectra from ACE with a simple model of interstellar propagation and solar modulation in order to place limits on the range of interstellar spectra that are compatible with both sets of data

A Single Scale Theory for Cold and Hot Dark Matter

We show that a recently proposed extension of the MSSM can provide a scenario where both the cold and hot dark matter of the universe owe their origin to a single scale connected with the breakdown of the global B-L symmetry. The susy partner of the majoron and the light Majorana neutrinos are the cold and hot dark matter candidates respectively in this model and their desired relative abundances emerge when the scale of B-L symmetry breaking is in the TeV range.Comment: UMD-PP-94-102 (latex file; 15 pages

Fabrication of a focusing soft X-ray collector payload

A large area X-ray focusing collector with arc minute resolution and a position sensitive detector capable of operating in the soft X-ray region was developed for use on sounding rockets in studying stellar X-ray sources. The focusing payload consists of the following components, which are described: (1) a crossed paraboloid mirror assembly; (2) an aspect camera and star tracker; (3) a focal plane assembly containing an imaging proportional counter and its preamplifiers, high voltage power supplies and gas system; (4) a fiducial system; and (5) housekeeping, data handling, instrumentation and telemetry electronics. The design, tests, and operation are described

Computable functions, quantum measurements, and quantum dynamics

We construct quantum mechanical observables and unitary operators which, if implemented in physical systems as measurements and dynamical evolutions, would contradict the Church-Turing thesis which lies at the foundation of computer science. We conclude that either the Church-Turing thesis needs revision, or that only restricted classes of observables may be realized, in principle, as measurements, and that only restricted classes of unitary operators may be realized, in principle, as dynamics.Comment: 4 pages, REVTE