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

Singularity Theory in Classical Cosmology

This paper compares recent approaches appearing in the literature on the singularity problem for space-times with nonvanishing torsion.Comment: 4 pages, plain-tex, published in Nuovo Cimento B, volume 107, pages 849-851, year 199

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

Spectral asymptotics of Euclidean quantum gravity with diff-invariant boundary conditions

A general method is known to exist for studying Abelian and non-Abelian gauge theories, as well as Euclidean quantum gravity, at one-loop level on manifolds with boundary. In the latter case, boundary conditions on metric perturbations h can be chosen to be completely invariant under infinitesimal diffeomorphisms, to preserve the invariance group of the theory and BRST symmetry. In the de Donder gauge, however, the resulting boundary-value problem for the Laplace type operator acting on h is known to be self-adjoint but not strongly elliptic. The latter is a technical condition ensuring that a unique smooth solution of the boundary-value problem exists, which implies, in turn, that the global heat-kernel asymptotics yielding one-loop divergences and one-loop effective action actually exists. The present paper shows that, on the Euclidean four-ball, only the scalar part of perturbative modes for quantum gravity are affected by the lack of strong ellipticity. Further evidence for lack of strong ellipticity, from an analytic point of view, is therefore obtained. Interestingly, three sectors of the scalar-perturbation problem remain elliptic, while lack of strong ellipticity is confined to the remaining fourth sector. The integral representation of the resulting zeta-function asymptotics is also obtained; this remains regular at the origin by virtue of a spectral identity here obtained for the first time.Comment: 25 pages, Revtex-4. Misprints in Eqs. (5.11), (5.14), (5.16) have been correcte

Novel features of the energy momentum tensor of a Casimir apparatus in a weak gravitational field

The influence of the gravity acceleration on the regularized energy-momentum tensor of the quantized electromagnetic field between two plane parallel conducting plates is derived. A perturbative expansion, to first order in the constant acceleration parameter, of the Green functions involved and of the energy-momentum tensor is derived by means of the covariant geodesic point splitting procedure. The energy-momentum tensor is covariantly conserved and satisfies the expected relation between gauge-breaking and ghost parts.Comment: 8 pages, based on a talk given by Luigi Rosa at the QFEXT07 Conference, Leipzig. Equation (13) and the formulae for rho and energy E stored in the Casimir device have been amended, jointly with related discussio

Periodic signals from the Circinus region: two new cataclysmic variables and the ultraluminous X-ray source candidate GC X-1

The examination of two 2010 Chandra ACIS exposures of the Circinus galaxy resulted in the discovery of two pulsators: CXO J141430.1-651621 and CXOU J141332.9-651756. We also detected 26-ks pulsations in CG X-1, consistently with previous measures. For ~40 other sources, we obtained limits on periodic modulations. In CXO J141430.1-651621, which is ~2 arcmin outside the Circinus galaxy, we detected signals at 6120(1) s and 64.2(5) ks. In the longest observation, the source showed a flux of ~1.1e-13 erg/cm^2/s (absorbed, 0.5-10 keV) and the spectrum could be described by a power-law with photon index ~1.4. From archival observations, we found that the luminosity is variable by ~50 per cent on time-scales of weeks-years. The two periodicities pin down CXO J141430.1-651621 as a cataclysmic variable of the intermediate polar subtype. The period of CXOU J141332.9-651756 is 6378(3) s. It is located inside the Circinus galaxy, but the low absorption indicates a Galactic foreground object. The flux was ~5e-14 erg/cm^2/s in the Chandra observations and showed ~50 per cent variations on weekly/yearly scales; the spectrum is well fit by a power law ~0.9. These characteristics and the large modulation suggest that CXOU J141332.9-651756 is a magnetic cataclysmic variable, probably a polar. For CG X-1, we show that if the source is in the Circinus galaxy, its properties are consistent with a Wolf-Rayet plus black hole binary. We consider the implications of this for ultraluminous X-ray sources and the prospects of Advanced LIGO and Virgo. In particular, from the current sample of WR-BH systems we estimate an upper limit to the detection rate of stellar BH-BH mergers of ~16 events per yr.Comment: 17 pages, 7 figures, 6 tables; accepted for publication in MNRA

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