Modelling the fair value of annuities contracts: the impact of interest rate risk and mortality risk

The purpose of this paper is to analyze the problem of the fair valuation of annuities contracts. The market consistent valuation of these products requires a pricing framework which includes the two main sources of risk affecting the value of the annuity, i.e. interest rate risk and mortality risk. As the IASB has not set any specific guidelines as to which models are the most appropriate for these risks, in this note we consider a range of different models calibrated with historical data. We calculate the fair value of the annuity as a portfolio of zero coupon bonds, each with maturity set equal to the date of the annuity payments; the weights in the portfolio are given by the survival probabilities. Moreover, we focus on the additional information provided by stochastic simulations in order to define a suitable risk margin. The nature of the risk margin is one of the main key issues concerning the IASB and Solvency project

New Developments in the Spectral Asymptotics of Quantum Gravity

A vanishing one-loop wave function of the Universe in the limit of small three-geometry is found, on imposing diffeomorphism-invariant boundary conditions on the Euclidean 4-ball in the de Donder gauge. This result suggests a quantum avoidance of the cosmological singularity driven by full diffeomorphism invariance of the boundary-value problem for one-loop quantum theory. All of this is made possible by a peculiar spectral cancellation on the Euclidean 4-ball, here derived and discussed.Comment: 7 pages, latex file. Paper prepared for the Conference "QFEXT05: Quantum Field Theory Under the Influence of External Conditions", Barcelona, September 5 - September 9, 2005. In the final version, the presentation has been further improved, and yet other References have been adde

Binary Fluids with Long Range Segregating Interaction I: Derivation of Kinetic and Hydrodynamic Equations

We study the evolution of a two component fluid consisting of ``blue'' and ``red'' particles which interact via strong short range (hard core) and weak long range pair potentials. At low temperatures the equilibrium state of the system is one in which there are two coexisting phases. Under suitable choices of space-time scalings and system parameters we first obtain (formally) a mesoscopic kinetic Vlasov-Boltzmann equation for the one particle position and velocity distribution functions, appropriate for a description of the phase segregation kinetics in this system. Further scalings then yield Vlasov-Euler and incompressible Vlasov-Navier-Stokes equations. We also obtain, via the usual truncation of the Chapman-Enskog expansion, compressible Vlasov-Navier-Stokes equations.Comment: TeX, 50 page

Spectral variability in Swift and Chandra observations of the Ultraluminous source NGC 55 ULX1

NGC 55 ULX1 is a bright Ultraluminous X-ray source located 1.78 Mpc away. We analysed a sample of 20 Swift observations, taken between 2013 April and August, and two Chandra observations taken in 2001 September and 2004 June. We found only marginal hints of a limited number of dips in the light curve, previously reported to occur in this source, although the uncertainties due to the low counting statistics of the data are large. The Chandra and Swift spectra showed clearly spectral variability which resembles those observed in other ULXs. We can account for this spectral variability in terms of changes in both the normalization and intrinsic column density of a two-components model consisting of a blackbody (for the soft component) and a multicolour accretion disc (for the hard component). We discuss the possibility that strong outflows ejected by the disc are in part responsible for such spectral changes.Comment: 9 pages, 6 figure; accepted to be published on MNRA

Cross Sections and Charged Pion Spectra in Proton-Carbon Interactions at 31 GeV/c

As neutrino long baseline experiments enter a new domain of precision, the careful study of systematic errors due to poor knowledge of production cross sections for pions and kaons require more dedicated measurements for precise neutrino flux predictions. The cosmic ray experiments require dedicated hadron production measurements to tune simulation models used to describe air shower profiles. Among other goals, the NA61/SHINE (SPS Heavy Ion and Neutrino Experiment) experiment at the CERN SPS aims at precision measurements (5% and below) for both neutrino and cosmic ray experiments: those will improve the prediction of the neutrino flux for the T2K experiment at J-PARC and the prediction of muon production in the propagation of air showers for the Auger and KASCADE experiments. NA61/SHINE took data during a pilot run in 2007 and in 2009 and 2010 with different carbon targets. The NA61/SHINE set-up and spectra for positive and negative pions obtained with the 2007 thin (4% interaction length) carbon target data are presented.Comment: To be published in the proceedings of WIN'11, Cape Town, South Africa, 31 January - 5 February 201

Swift monitoring of IGR J16418-4532

We report on the Swift observations of the candidate supergiant fast X-ray transient (SFXT) IGR J16418-4532, which has an orbital period of ~3.7 d. Our monitoring, for a total of ~43 ks, spans over three orbits and represents the most intense and complete sampling along the orbital period of the light curve of this source. If one assumes a circular orbit, the X-ray emission from this source can be explained by accretion from a spherically symmetric clumpy wind from a blue supergiant, composed of clumps with different masses, ranging from ~5x10^16 g to 10^21g.Comment: 4 pages; Proceedings, 5th International Symposium on High-Energy Gamma-Ray Astronomy, (Gamma2012) Heidelberg, Germany, July 9-13th, 201

Discovery of a 6.4 h black hole binary in NGC 4490

We report on the discovery with Chandra of a strong modulation (~90% pulsed fraction) at ~6.4 h from the source CXOU J123030.3+413853 in the star-forming, low-metallicity spiral galaxy NGC 4490, which is interacting with the irregular companion NGC 4485. This modulation, confirmed also by XMM-Newton observations, is interpreted as the orbital period of a binary system. The spectra from the Chandra and XMM-Newton observations can be described by a power-law model with photon index ~1.5. During these observations, which span from 2000 November to 2008 May, the source showed a long-term luminosity variability by a factor of ~5, between ~2E+38 and 1.1E+39 erg/s (for a distance of 8 Mpc). The maximum X-ray luminosity, exceeding by far the Eddington limit of a neutron star, indicates that the accretor is a black hole. Given the high X-ray luminosity, the short orbital period and the morphology of the orbital light curve, we favour an interpretation of CXOU J123030.3+413853 as a rare high-mass X-ray binary system with a Wolf-Rayet star as a donor, similar to Cyg X-3. This would be the fourth system of this kind known in the local Universe. CXOU J123030.3+413853 can also be considered as a transitional object between high mass X-ray binaries and ultraluminous X-ray sources (ULXs), the study of which may reveal how the properties of persistent black-hole binaries evolve entering the ULX regime.Comment: Fig. 1 in reduced quality; minor changes to match the MNRAS versio

An introduction to quantum gravity

After an overview of the physical motivations for studying quantum gravity, we reprint THE FORMAL STRUCTURE OF QUANTUM GRAVITY, i.e. the 1978 Cargese Lectures by Professor B.S. DeWitt, with kind permission of Springer. The reader is therefore introduced, in a pedagogical way, to the functional integral quantization of gravitation and Yang-Mills theory. It is hoped that such a paper will remain useful for all lecturers or Ph.D. students who face the task of introducing (resp. learning) some basic concepts in quantum gravity in a relatively short time. In the second part, we outline selected topics such as the braneworld picture with the same covariant formalism of the first part, and spectral asymptotics of Euclidean quantum gravity with diffeomorphism-invariant boundary conditions. The latter might have implications for singularity avoidance in quantum cosmology.Comment: 68 pages, Latex file. Sections from 2 to 17 are published thanks to kind permission of Springe