Measures of financial risks and market crashes

The problem of particular importance in financial risk management is forecasting the magnitude of a market crash. We address this problem using statistical inference on heavy–tailed distributions. Our approach involves accurate estimates of the tail index, extreme quantiles, and the mean excess function. We apply our approach to real financial data, and argue that the September 2001 crash had two components: one (systematic) could be predicted, while another (non–systematic) was due to the shock of the event. We present empirical evidence that the degree of tail heaviness can change considerably as one switches to less frequent data. This fact has important implications to the problem of estimating financial risks

On the length of the longest head run

We evaluate the accuracy of approximation to the distribution of the length of the longest head run in a Markov chain with a discrete state space. An estimate of the accuracy of approximation in terms of the total variation distance is established for the first time

On the accuracy of multivariate compound Poisson approximation

We present multivariate generalizations of some classical results on the accuracy of Poisson approximation for the distribution of a sum of 0–1 random variables. A multivariate generalization of Bradley's theorem (Michigan Math. J. 30 (1983) 69) is established as well

Measurement of the Bottom-Strange Meson Mixing Phase in the Full CDF Data Set

We report a measurement of the bottom-strange meson mixing phase \beta_s using the time evolution of B0_s -> J/\psi (->\mu+\mu-) \phi (-> K+ K-) decays in which the quark-flavor content of the bottom-strange meson is identified at production. This measurement uses the full data set of proton-antiproton collisions at sqrt(s)= 1.96 TeV collected by the Collider Detector experiment at the Fermilab Tevatron, corresponding to 9.6 fb-1 of integrated luminosity. We report confidence regions in the two-dimensional space of \beta_s and the B0_s decay-width difference \Delta\Gamma_s, and measure \beta_s in [-\pi/2, -1.51] U [-0.06, 0.30] U [1.26, \pi/2] at the 68% confidence level, in agreement with the standard model expectation. Assuming the standard model value of \beta_s, we also determine \Delta\Gamma_s = 0.068 +- 0.026 (stat) +- 0.009 (syst) ps-1 and the mean B0_s lifetime, \tau_s = 1.528 +- 0.019 (stat) +- 0.009 (syst) ps, which are consistent and competitive with determinations by other experiments.Comment: 8 pages, 2 figures, Phys. Rev. Lett 109, 171802 (2012

Effect of event selection on jetlike correlation measurement in d+Au collisions at sNN=200 GeV

AbstractDihadron correlations are analyzed in sNN=200 GeV d+Au collisions classified by forward charged particle multiplicity and zero-degree neutral energy in the Au-beam direction. It is found that the jetlike correlated yield increases with the event multiplicity. After taking into account this dependence, the non-jet contribution on the away side is minimal, leaving little room for a back-to-back ridge in these collisions

J/ψ polarization in p+p collisions at s=200 GeV in STAR

AbstractWe report on a polarization measurement of inclusive J/ψ mesons in the di-electron decay channel at mid-rapidity at 2<pT<6 GeV/c in p+p collisions at s=200 GeV. Data were taken with the STAR detector at RHIC. The J/ψ polarization measurement should help to distinguish between different models of the J/ψ production mechanism since they predict different pT dependences of the J/ψ polarization. In this analysis, J/ψ polarization is studied in the helicity frame. The polarization parameter λθ measured at RHIC becomes smaller towards high pT, indicating more longitudinal J/ψ polarization as pT increases. The result is compared with predictions of presently available models