Modeling operational risk data reported above a time-varying threshold

Typically, operational risk losses are reported above a threshold. Fitting data reported above a constant threshold is a well known and studied problem. However, in practice, the losses are scaled for business and other factors before the fitting and thus the threshold is varying across the scaled data sample. A reporting level may also change when a bank changes its reporting policy. We present both the maximum likelihood and Bayesian Markov chain Monte Carlo approaches to fitting the frequency and severity loss distributions using data in the case of a time varying threshold. Estimation of the annual loss distribution accounting for parameter uncertainty is also presented

Topologically Induced Optical Activity in Graphene-Based Meta-Structures

Non-reciprocity and asymmetric transmission in optical and plasmonic systems is a key element for engineering the one-way propagation structures for light manipulation. Here we investigate topological nanostructures covered with graphene-based meta-surfaces, which consist of a periodic pattern of sub-wavelength stripes of graphene winding around the (meta-) tube or (meta-)torus. We establish the relation between the topological and plasmonic properties in these structures, as justified by simple theoretical expressions. Our results demonstrate how to use strong asymmetric and chiral plasmonic responses to tailor the electrodynamic properties in topological meta-structures. Cavity resonances formed by elliptical and hyperbolic plasmons in meta-structures are sensitive to the one-way propagation regime in a finite length (Fabry-Perot-like) meta-tube and display the giant mode splitting in a (Mach-Zehnder-like) meta-torus.Comment: 20 pages, 5 figures + TOC figure, accepted by ACS Photonic

Parametric frequency mixing in the magneto-elastically driven FMR-oscillator

We demonstrate the nonlinear frequency conversion of ferromagnetic resonance (FMR) frequency by optically excited elastic waves in a thin metallic film on dielectric substrates. Time-resolved probing of the magnetization directly witnesses magneto-elastically driven second harmonic generation, sum- and difference frequency mixing from two distinct frequencies, as well as parametric downconversion of each individual drive frequency. Starting from the Landau-Lifshitz-Gilbert equations, we derive an analytical equation of an elastically driven nonlinear parametric oscillator and show that frequency mixing is dominated by the parametric modulation of FMR frequency

On a class of distributions stable under random summation

We investigate a family of distributions having a property of stability-under-addition, provided that the number $\nu$ of added-up random variables in the random sum is also a random variable. We call the corresponding property a \,$\nu$-stability and investigate the situation with the semigroup generated by the generating function of $\nu$ is commutative. Using results from the theory of iterations of analytic functions, we show that the characteristic function of such a $\nu$-stable distribution can be represented in terms of Chebyshev polynomials, and for the case of $\nu$-normal distribution, the resulting characteristic function corresponds to the hyperbolic secant distribution. We discuss some specific properties of the class and present particular examples.Comment: 12 pages, 1 figur

Ultrafast laser-induced phenomena in solids studied by time-resolved interferometry

In this work we have presented the technique for ultrafast time-resolved imaging interferometry and its application to the two di?erent problems of laser-matter interaction: femtosecond laser ablation of absorbing solids and optical breakdown in dielectrics. The presented detailed analysis of the technique including the optical design of the Michelson- and Mach-Zehnder-type imaging interferometers, analysis of the image formation and its relation to the 2D-Fourier-transform algorithm, artifacts in the reconstructed phase and amplitude maps as well as the physical interpretation of phase measurements represent a signi?cant development in the ?eld of time-resolved imaging interferometry. Without such analysis the results of interferometric measurements would be not so valuable and their interpretation not unique. Interferometric measurements at an ablating GaAs-surface allowed us to directly observe several types of transient surface deformations of laser-excited material both below and above the ablation threshold. The results of interferometric measurements support the theoretically predicted inhomogeneous bubble-like internal structure of an ablating layer. The expansion velocity of a hot pressurized laser-molten layer of material is shown to slow down during the ?rst few hundred of picoseconds of expansion, which strongly indicates the build up of tensile stresses in a liquid upon expansion (negative pressure). The observed extremely slow large-amplitude reversible surface deformations could be explained by the frustrated liquid-gas phase transition. This motivates further theoretical investigations of femtosecond laser ablation, which must be focused on the properties of metastable liquids under negative pressure. The variety of new ?ndings deduced from the measurements in GaAs motivate further interferometric studies in di?erent materials and possibly using slightly di?erent experimental con?gurations. As in the case of the universal Newton fringe phenomena we anticipate transient surface deformations to be driven by a material-independent mechanism. Finally, the price/quality ratio of interferometric measurements at ablating surfaces appeared to be very attractive and the chances of fully understanding the basic physical mechanisms of femtosecond laser ablation in the near future are very good. Interferometric measurements in transmission made with the help of imaging Mach-Zehnder-type interferometry aimed to clarify the ionization mechanisms in dielectrics irradiated by single intense femtosecond laser pulses. Signi?cant e?orts have been made to get rid of the propagation e?ects such as self-phase modulation and selffocusing, which only represent additional complications in these types of experi-ments. The 50 fs-time resolution achieved allowed us to follow the extremely fast dynamics of free carriers in sapphire and fused silica just after excitation. We were able to clearly demonstrate that at relatively low intensities below 10 TW/cm2 the dominant ionization mechanism is the 6-photon ionization, which is polarization dependent. The surface breakdown threshold does also slightly depend on laser polarization. The cross-sections of multiphoton ionization have been determined with an accuracy, which is much better than in all previously reported studies. However, at high intensities the spatial averaging in the propagation direction has been shown to be important. The comparison of experimental data with the results of model calculations of 1D-pulse propagation in dielectrics suggests that in fused silica the multiphoton ionization might be the dominant ionization mechanism up to the surface breakdown threshold, whereas for sapphire the ionization mechanism must be di?erent in the pre-breakdown regime. The attempts to compare the experimental data with the predictions of Keldyshs theory of photoionization were not successful. Without redoing Keldyshs calculations we were able to understand the limitations and assumptions behind his model calculations. Whereas Keldyshs general approach is very interesting and elegant from a theoretical point of view, his model calculations could not be applied for the given experimental situation. The most important problem is that high-?eld carrier transport in dielectrics induces extremely fast electron-lattice collisions, which are not included in Keldyshs approach. Finally, the price/quality ratio of interferometric measurements in dielectrics appeared to be rather moderate and the chances of understanding the ionization mechanisms in dielectrics in the pre-breakdown regime in the near future are slim

Nonlinear surface magneto-plasmonics in Kretschmann multilayers

The nonlinear magneto-plasmonics aims to utilize plasmonic excitations to control the mechanisms and taylor the efficiencies of the non-linear light frequency conversion at the nanoscale. We investigate the mechanisms of magnetic second harmonic generation in hybrid gold-cobalt-silver multilayer structures, which support propagating surface plasmon polaritons at both fundamental and second harmonic frequencies. Using magneto-optical spectroscopy in Kretschmann geometry, we show that the huge magneto-optical modulation of the second harmonic intensity is dominated by the excitation of surface plasmon polaritons at the second harmonic frequency, as shown by tuning the optical wavelength over the spectral region of strong plasmonic dispersion. Our proof-of-principle experiment highlights bright prospects of nonlinear magneto-plasmonics and contributes to the general understanding of the nonlinear optics of magnetic surfaces and interfaces.Comment: Main Manuscript: 5 pages, 3 figures. Supplementary Information: 10 pages, 7 figure