Sensitivity of risk measures with respect to the normal approximation of total claim distributions

A simple and commonly used method to approximate the total claim distribution of a (possibly weakly dependent) insurance collective is the normal approximation. In this article, we investigate the error made when the normal approximation is plugged in a fairly general distribution-invariant risk measure. We focus on the rate of convergence of the error relative to the number of clients, we specify the relative error’s asymptotic distribution, and we illustrate our results by means of a numerical example. Regarding the risk measure, we take into account distortion risk measures as well as distribution-invariant coherent risk measures.     

Effects of dynamical couplings in IR spectra of the hydrogen bond in N-phenylacrylamide crystals

This article presents the investigation results of the polarized IR spectra of the hydrogen bond in N-phenylacrylamide crystals measured in the frequency range of the proton and deuteron, ν(N-H) and ν(N-D), stretching vibration bands. The basic spectral properties of the crystals were interpreted quantitatively in terms of the "strong-coupling" theory. The proposed model of the centrosymmetric dimer of hydrogen bonds facilitated the explanation of the well-developed, two-branch structure of the ν(N-H) and ν(N-D) bands as well as the isotopic dilution effects in the spectra. The vibronic mechanism of the generation of the long-wave branch of the ν(N-H) band ascribed to the excitation of the totally symmetric proton vibration was elucidated. The complex fine structure pattern of ν(N-H) and ν(N-D) bands in N-phenylacrylamide spectra in comparison with the spectra of other secondary amide crystals (e.g., N-methylacetamide and acetanilide) can be accounted for in terms of the vibronic model for the forbidden transition breaking in the dimers. On the basis of the linear dichroic and temperature effects in the polarized IR spectra of N-phenylacrylamide crystals, the H/D isotopic "self-organization" effects were revealed.     

Electron-induced phase transition in hydrogen-bonded solid-state 2-pyridone

This paper presents the results of experimental studies of hydrogen-bonded 2-pyridone crystal IR spectra. Spectral studies have demonstrated the existence of two anhydrous solid-state phases of each compound, namely the α and the β phases. Hydrogen bonds in the high-temperature α phase of these crystals have been estimated to be 40% stronger than the hydrogen bonds in the β phase, which are stable at room temperature. The mechanism of the phase transition in the solid-state 2-pyridone is proposed on the basis of the IR spectral data. This was possible by taking into account small changes in the geometry of heterocyclic molecular skeletons, which accompany the electron density redistribution in the hydrogen bonds occurring during the transition. The phase transition is connected with a partial change in the hydrogen bond nature from the N(+)-H···O(-) in the α phase, to the N-H···O hydrogen bonds in the β phase crystals.     

Complete assignment of the vibrational modes of C60 by inelastic neutron scattering spectroscopy and periodic-DFT

In this paper we exploit the complementarity of inelastic neutron scattering (INS), infrared and Raman spectroscopies with ab initio calculations to generate an updated assignment of the vibrational modes of C(60). We have carried out periodic-DFT calculations of the high temperature face centred cubic phase modelled as the standard structure and also of the low temperature simple cubic phase, the latter for the first time. Our assignment differs from all previous work, however, it is the only one that is able to successfully reproduce the INS spectrum in terms of both transition energies and intensities. In addition to the INS spectrum we are also able to quantitatively simulate the major features of the infrared and Raman spectra in the high temperature phase and the infrared spectrum in the low temperature phase.     

The curse of dimensionality for the class of monotone functions and for the class of convex functions

We study the integration and approximation problems for monotone or convex bounded functions that depend on $d$ variables, where $d$ can be arbitrarily large. We consider the worst case error for algorithms that use finitely many function values. We prove that these problems suffer from the curse of dimensionality. That is, one needs exponentially many (in $d$) function values to achieve an error $\epsilon$.     

Geometric properties of F-normed Orlicz spaces

Aequationes mathematicae - The paper deals with F-normed functions and sequence spaces. First, some general results on such spaces are presented. But most of the results in this paper concern...     

Review of fluorescence anisotropy decay analysis by frequency-domain fluorescence spectroscopy

This didactic paper summarizes the mathematical expressions needed for analysis of fluorescence anisotropy decays from polarized frequency-domain fluorescence data. The observed values are the phase angle difference between the polarized components of the emission and the modulated anisotropy, which is the ratio of the polarized and amplitude-modulated components of the emission. This procedure requires a separate measurement of the intensity decay of the total emission. The expressions are suitable for any number of exponential components in both the intensity decay and the anisotropy decay. The formalism is generalized for global analysis of anisotropy decays measured at different excitation wavelengths and for different intensity decay times as the result of quenching. Additionally, we describe the expressions required for associated anisotropy decays, that is, anisotropy decays where each correlation time is associated with a decay time present in the anisotropy decay. And finally, we present expressions appropriate for distributions of correlation times. This article should serve as a reference for researchers using frequency-domain fluorometry.     

Three-photon-induced fluorescence of diphenylhexatriene in solvents and lipid bilayers

We observed the emission of l,6-diphenyl-l,3,5-hexatriene (DPH) when excited with the fundamental output of a fs Ti:sapphire laser at 860 nm. The emission spectra of DPH were identical to that observed for one-photon excitation at 287 nm. The dependence of the DPH emission intensity on laser power was cubic, indicating three-photon excitation of DPH at 860 nm. At a shorter wavelength of 810 nm, the dependence on laser power was quadratic, indicating a two-photon process. At an intermediate wavelength of 830 nm the mode of excitation was a mixture of two- and three-photon excitation. At 830 nm the anisotropy is no longer a molecular parameter, and the mode of excitation and anisotropy of DPH depends on laser power. Frequency-domain anisotropy decays of DPH in triacetin revealed the same rotational correlation times for two- and three-photon excitation. However, the time 0 anisotropy of DPH was larger for three-photon excitation than for two-photon excitation. Steady-state anisotropy data for DPH-labeled membranes revealed the same transition temperature for one- and three-photon excitation. These anisotropy data indicate that membrane heating was not significant with three-photon excitation and that three-photon excitation may thus be of practical usefulness in fluorescence spectroscopy and microscopy of membranes.     

Bayesian parameter inference for models of the Black and Scholes type

In this paper, we describe a general method for constructing the posterior distribution of the mean and volatility of the return of an asset satisfying dS=SdX for some simple models of X. Our framework takes as inputs the prior distributions of the parameters of the stochastic process followed by the underlying, as well as the likelihood function implied by the observed price history for the underlying. As an application of our framework, we compute the value at risk (VaR) and conditional VaR (CVaR) measures for the changes in the price of an option implied by the posterior distribution of the volatility of the underlying. The implied VaR and CVaR are more conservative than their classical counterpart, since it takes into account the estimation risk that arises due to parameter uncertainty. Copyright © 2008 John Wiley & Sons, Ltd.