A gravity model of mortality rates for two related populations

The mortality rate dynamics between two related but different-sized populations are modeled consistently using a new stochastic mortality model that we call the gravity model. The larger population is modeled independently, and the smaller population is modeled in terms of spreads (or deviations) relative to the evolution of the former, but the spreads in the period and cohort effects between the larger and smaller populations depend on gravity or spread reversion parameters for the two effects. The larger the two gravity parameters, the more strongly the smaller population’s mortality rates move in line with those of the larger population in the long run. This is important where it is believed that the mortality rates between related populations should not diverge over time on grounds of biological reasonableness. The model is illustrated using an extension of the Age-Period-Cohort model and mortality rate data for English and Welsh males representing a large population and the Continuous Mortality Investigation assured male lives representing a smaller related population.Gravity model; mortality rates; related populations

The abundance of moduli, modulini and gravitinos produced by the vacuum fluctuation

Moduli, modulini and the gravitino have gravitational-strength interactions, and thermal collisions after reheating create all of them with roughly the same abundance. With their mass of order 100\GeV, corresponding to gravity-mediated supersymmetry breaking, this leads to the well-known bound \gamma T\sub R\lsim 10^9\GeV on the reheat temperature, where $\gamma\leq 1$ is the entropy dilution factor. The vacuum fluctuation also creates these particles, with abundance determined by the solution of the equation for the mode function. Taking the equation in each case to be the one corresponding to a free field, we consider carefully the behaviour of the effective mass during the crucial era after inflation. It may have a rapid oscillation, which does not however affect the particle abundance. Existing estimates are confirmed; the abundance of modulini and (probably) of moduli created from the vacuum is less than from thermal collisions, but the abundance of gravitinos may be much bigger, leading to a tighter bound on $T\sub R$ if supersymmetry breaking is gravity-mediated. It is noted that in the case of gauge-mediated supersymmetry breaking, the abundance of the gravitino may be sufficient to make it a dark matter candidate.Comment: 14 pages. v3 as it will appear in PL

Longevity hedging 101: A framework for longevity basis risk analysis and hedge effectiveness

Basis risk is an important consideration when hedging longevity risk with instruments based on longevity indices, since the longevity experience of the hedged exposure may differ from that of the index. As a result, any decision to execute an index-based hedge requires a framework for (1) developing an informed understanding of the basis risk, (2) appropriately calibrating the hedging instrument, and (3) evaluating hedge effectiveness. We describe such a framework and apply it to a U.K. case study, which compares the population of assured lives from the Continuous Mor- tality Investigation with the England and Wales national population. The framework is founded on an analysis of historical experience data, together with an appreciation of the contextual relationship between the two related populations in social, economic, and demographic terms. Despite the different demographic profiles, the case study provides evidence of stable long-term relationships between the mortality experiences of the two populations. This suggests the important result that high levels of hedge effectiveness should be achievable with appropriately cali- brated, static, index-based longevity hedges. Indeed, this is borne out in detailed calculations of hedge effectiveness for a hypothetical pension portfolio where the basis risk is based on the case study. A robustness check involving populations from the United States yields similar results.Longevity risk; basis risk; hedge effectiveness

Multiple indices of diffusion identifies white matter damage in mild cognitive impairment and Alzheimer's disease

The study of multiple indices of diffusion, including axial (DA), radial (DR) and mean diffusion (MD), as well as fractional anisotropy (FA), enables WM damage in Alzheimer's disease (AD) to be assessed in detail. Here, tract-based spatial statistics (TBSS) were performed on scans of 40 healthy elders, 19 non-amnestic MCI (MCIna) subjects, 14 amnestic MCI (MCIa) subjects and 9 AD patients. Significantly higher DA was found in MCIna subjects compared to healthy elders in the right posterior cingulum/precuneus. Significantly higher DA was also found in MCIa subjects compared to healthy elders in the left prefrontal cortex, particularly in the forceps minor and uncinate fasciculus. In the MCIa versus MCIna comparison, significantly higher DA was found in large areas of the left prefrontal cortex. For AD patients, the overlap of FA and DR changes and the overlap of FA and MD changes were seen in temporal, parietal and frontal lobes, as well as the corpus callosum and fornix. Analysis of differences between the AD versus MCIna, and AD versus MCIa contrasts, highlighted regions that are increasingly compromised in more severe disease stages. Microstructural damage independent of gross tissue loss was widespread in later disease stages. Our findings suggest a scheme where WM damage begins in the core memory network of the temporal lobe, cingulum and prefrontal regions, and spreads beyond these regions in later stages. DA and MD indices were most sensitive at detecting early changes in MCIa

Inflation and Supersymmetry Breaking

We study the connection between inflation and supersymmetry breaking in the context of an O'Raifeartaigh model which can account for both hybrid inflation and a true vacuum where supersymmetry is spontaneously broken. For a weakly coupled inflaton field, the dynamics during the inflationary phase can be determined by the supersymmetry breaking scale $M_S\sim 10^{10}$ GeV, even if $H_I >> m_{3/2}$. The spectrum of density fluctuations is then almost scale invariant, with a spectral index $n-1={\cal O}(M_G^2/M_P^2)$. The mass parameter $M_G$ of the O'Raifeartaigh model is determined by the COBE normalization for the cosmic microwave background to be the grand unification scale, $M_G \sim 10^{16}$ GeV.Comment: 13 pages, 2 figures; one paragraph and references added, to appear in PL

Longevity hedge effectiveness: A decomposition

We use a case study of a pension plan wishing to hedge the longevity risk in its pension liabilities at a future date. The plan has the choice of using either a customised hedge or an index hedge, with the degree of hedge effectiveness being closely related to the correlation between the value of the hedge and the value of the pension liability. The key contribution of this paper is to show how correlation and, therefore, hedge effectiveness can be broken down into contributions from a number of distinct types of risk factors. Our decomposition of the correlation indicates that population basis risk has a significant influence on the correlation. But recalibration risk as well as the length of the recalibration window are also important, as is cohort effect uncertainty. Having accounted for recalibration risk, additional parameter uncertainty has only a marginal impact on hedge effectiveness. Finally, the inclusion of Poisson risk only starts to become significant when the smaller population falls below about 10,000 members over age 50. Our case study shows that, at least for medium and large pension plans, longevity risk can be substantially hedged using index hedges as an alternative to customised longevity hedges. As a consequence, when the hedger's population involves more than about 10,000 members over age 50, index longevity hedges (in conjunction with the other components of an ALM strategy) can provide an effective and lower cost alternative to both a full buy-out of pension liabilities or even to a strategy using customised longevity hedges

Cosmology with a TeV mass GUT Higgs

The most natural way to break the GUT gauge symmetry is with a Higgs field whose vacuum expectation value is of order 10^{16}\,\mbox{GeV} but whose mass is of order $10^2$ to 10^3\,\mbox{GeV}. This can lead to a cosmological history radically different from what is usually assumed to have occurred between the standard inflationary and nucleosynthesis epochs, which may solve the gravitino and Polonyi/moduli problems in a natural way.Comment: 4 pages, revte

The Sewers, the City, the Tower: Pynchon's V., Fausto's Confessions, and Yeats's A Vision

peer-reviewedThis article examines the connections between Thomas Pynchon's V. and the work of W. B. Yeats, arguing that it is not only Yeats as poet, but also Yeats as mage, who interests Pynchon. It shows what part is played in V. by the concepts developed by Yeats in his works Per Amica Silentia Lunae and A Vision - the symbol of interlocking gyres, the twenty-eight phases, the Great Wheel, and the Anima Mundi, or soul of the world. It argues that in the course of the chapter "Confessions of Fausto Maijstral," Pynchon uses the destruction of the Maltese city of Valletta first to both represent and criticize the abstraction of Yeats's Byzantium and second, through the figure of the child poet, to recast Yeats's Anima Mundi as a textual realm open to and changing with the demands and experiences of the present.ACCEPTEDpeer-reviewe