Actuaries must model mortality to understand, manage and price risk. Continuous-time methods offer considerable practical benefits to actuaries analysing portfolio mortality experience. This paper discusses six categories of advantage: (i) reflecting the reality of data produced by everyday business practices, (ii) modelling rapid changes in risk, (iii) modelling time- and duration-varying risk, (iv) competing risks, (v) data-quality checking and (vi) management information. Specific examples are given where continuous-time models are more useful in practice than discrete-time models.

We reprise some common statistical models for actuarial mortality analysis using grouped counts. We then discuss the benefits of building mortality models from the most elementary items. This has two facets. First, models are better based on the mortality of individuals, rather than groups. Second, models are better defined in continuous time, rather than over fixed intervals like a year. We show how Poisson-like likelihoods at the “macro” level are built up by product integration of sequences of infinitesimal Bernoulli trials at the “micro” level. Observed data is represented through a stochastic mortality hazard rate, and counting processes provide the natural notation for left-truncated and right-censored actuarial data, individual or age-grouped. Together these explain the “pseudo-Poisson” behaviour of survival model likelihoods.

Recent changes to US research funding are having far-reaching consequences that imperil the integrity of science and the provision of care to vulnerable populations. Resisting these changes, the BJPsych Portfolio reaffirms its commitment to publishing mental science and advancing psychiatric knowledge that improves the mental health of one and all.

Stochastic mortality models are important for a variety of actuarial tasks, from best-estimate forecasting to assessment of risk capital requirements. However, the mortality shock associated with the Covid-19 pandemic of 2020 distorts forecasts by (i) biasing parameter estimates, (ii) biasing starting points, and (iii) inflating variance. Stochastic mortality models therefore require outlier-robust methods for forecasting. Objective methods are required, as outliers are not always obvious on visual inspection. In this paper we look at the robustification of three broad classes of forecast: univariate time indices (such as in the Lee-Carter and APC models); multivariate time indices (such as in the Cairns-Blake-Dowd and newer Tang-Li-Tickle model families); and penalty projections (such as with the 2D P-spline model). In each case we identify outliers using quantitative methods, then co-estimate outlier effects along with other parameters. Doing so removes the bias and distortion to the forecast caused by a mortality shock, while providing a robust starting point for projections. Illustrations are given for various models in common use.

We perform direct numerical simulations of soluble bubbles dissolving in a Taylor–Couette (TC) flow reactor with a radius ratio of $\eta =0.5$ and Reynolds number in the range $0 \leq Re \leq 5000$, which covers the main regimes of this flow configuration, up to fully turbulent Taylor vortex flow. The numerical method is based on a geometric volume-of-fluid framework for incompressible flows coupled with a phase-change solver that ensures mass conservation of the soluble species, whilst boundary conditions on solid walls are enforced through an embedded boundary approach. The numerical framework is validated extensively against single-phase TC flows and competing mass transfer in multicomponent mixtures for an idealised infinite cylinder and for a bubble rising in a quiescent liquid. Our results show that when bubbles in a TC flow are mainly driven by buoyancy, theoretical formulae derived for spherical interfaces on a vertical trajectory still provide the right fundamental relationship between the bubble Reynolds and Sherwood numbers, which reduces to $Sh \propto \sqrt {Pe}$ for large Péclet values. For bubbles mainly transported by TC flows, the dissolution of bubbles depend on the TC Reynolds number and, for the turbulent configurations, we show that the smallest characteristic turbulent scales control mass transfer, in agreement with the small-eddy model of Lamont & Scott (AIChE J., vol. 16, 1970, pp. 513–519). Finally, the interaction between two aligned bubbles is investigated and we show that a significant increase in mass transfer can be obtained when the rotor of the apparatus is operated at larger speeds.

The purpose of this report is to describe the appropriate use of indices relating to crystallinity, such as the ‘crystallinity index’, the ‘Hinckley index’, the ‘Kübler index’, and the ‘Árkai index’. A ‘crystalline’ solid is defined as a solid consisting of atoms, ions or molecules packed together in a periodic arrangement. A ‘crystallinity index’ is purported to be a measure of crystallinity, although there is uncertainty about what this means (see below). This report discusses briefly the nature of order, disorder and crystallinity in phyllosilicates and discusses why the use of a ‘crystallinity index’ should be avoided. If possible, it is suggested that indices be referred to using the name of the author who originally described the parameter, e.g. ‘Hinckley index’ or ‘Kübler index’, or in honor of a researcher who investigated the importance of the parameter extensively, e.g. ‘Árkai index’.

Tang et al. (2022) propose a new class of models for stochastic mortality modelling using Hermite splines. There are four useful features of this class that are worth emphasising. First, for single-sex datasets, this new class of projection models can be fitted as a generalised linear model. Second, these models can automatically extrapolate mortality rates to ages above the maximum age of the data set. Third, simpler sub-variants of the models exist for forecasting when one of the variables lacks a clear drift. Finally, a minor reparameterisation increases the quality of long-range forecasts of period mortality.

The fight against ecological degradation “has become a generalized policy demand of the whole society,” declared Marcelo Javelly Girard, Mexico's Secretary of Urban Development and Ecology. Addressing the Mexican Cabinet and hundreds of dignitaries attending Mexico's Primera Reunión Nacional de Ecología in June of 1984, Javelly Girard thus placed environmental concerns on President Miguel de la Madrid's official policy agenda. Appropriately convened in Mexico City (the world's fifth-most-polluted city by the Mexican government's own reckoning), the congress climaxed two years of effort by the de la Madrid administration to promote public environmental awareness as part of its national development program.

Seabirds are declining globally and are one of the most threatened groups of birds. To halt or reverse this decline they need protection both on land and at sea, requiring site-based conservation initiatives based on seabird abundance and diversity. The Important Bird and Biodiversity Area (IBA) programme is a method of identifying the most important places for birds based on globally agreed standardised criteria and thresholds. However, while great strides have been made identifying terrestrial sites, at-sea identification is lacking. The Chagos Archipelago, central Indian Ocean, supports four terrestrial IBAs (tIBAs) and two proposed marine IBAs (mIBAs). The mIBAs are seaward extensions to breeding colonies based on outdated information and, other types of mIBA have not been explored. Here, we review the proposed seaward extension mIBAs using up-to-date seabird status and distribution information and, use global positioning system (GPS) tracking from Red-footed Booby Sula sula – one of the most widely distributed breeding seabirds on the archipelago – to identify any pelagic mIBAs. We demonstrate that due to overlapping boundaries of seaward extension to breeding colony and pelagic areas of importance there is a single mIBA in the central Indian Ocean that lays entirely within the Chagos Archipelago Marine Protected Area (MPA). Covering 62,379 km2 it constitutes ~10% of the MPA and if designated, would become the 11th largest mIBA in the world and 4th largest in the Indian Ocean. Our research strengthens the evidence of the benefits of large-scale MPAs for the protection of marine predators and provides a scientific foundation stone for marine biodiversity hotspot research in the central Indian Ocean.

The COVID-19 pandemic requires that actuaries track short-term mortality fluctuations in the portfolios they manage. This demands methods that not only operate over much shorter time periods than a year but that also deal with reporting delays. In this paper, we consider a semi-parametric approach for tracking portfolio mortality levels in continuous time. We identify both seasonal patterns and mortality shocks, thus providing a comparison benchmark for the impact of COVID-19 in terms of a portfolio’s own past experience. A parametric model is presented to allow for the average impact of seasonal variation and also reporting delays. We find that an estimate of mortality reporting delays can be made from a single extract of experience data. This can be used to forecast unreported deaths and improve estimates of recent mortality levels. Results are given for annuity portfolios in France, the UK and the USA.

The COVID-19 pandemic creates a challenge for actuaries analysing experience data that include mortality shocks. Without sufficient local flexibility in the time dimension, any analysis based on the most recent data will be biased by the temporarily higher mortality. Also, depending on where the shocks sit in the exposure period, any attempt to identify mortality trends will be distorted. We present a methodology for analysing portfolio mortality data that offer local flexibility in the time dimension. The approach permits the identification of seasonal variation, mortality shocks and occurred-but-not reported deaths (OBNR). The methodology also allows actuaries to measure portfolio-specific mortality improvements. Finally, the method assists actuaries in determining a representative mortality level for long-term applications like reserving and pricing, even in the presence of mortality shocks. Results are given for a mature annuity portfolio in the UK, which suggest that the Bayesian information criterion is better for actuarial model selection in this application than Akaike’s information criterion.

Parametric mortality models permit detailed analysis of risk factors for actuarial work. However, finite data volumes lead to uncertainty over parameter estimates, which in turn gives rise to mis-estimation risk of financial liabilities. Mis-estimation risk can be assessed on a run-off basis by valuing the liabilities with alternative parameter vectors consistent with the covariance matrix. This run-off approach is especially suitable for tasks like pricing portfolio transactions, such as bulk annuities, longevity swaps or reinsurance treaties. However, a run-off approach does not fully meet the requirements of regulatory regimes that view capital requirements through the prism of a finite horizon, such as Solvency II’s one-year approach. This paper presents a methodology for viewing mis-estimation risk over a fixed time frame, and results are given for a specimen portfolio. As expected, we find that time-limited mis-estimation capital requirements increase as the horizon is lengthened or the discount rate is reduced. However, we find that much of the so-called mis-estimation risk in a one-year value-at-risk assessment can actually be driven by idiosyncratic variation, rather than parameter uncertainty. This counter-intuitive result stems from trying to view a long-term risk through a short-term window. As a result, value-at-risk mis-estimation reserves are strongly correlated with idiosyncratic risk. We also find that parsimonious models tend to produce lower mis-estimation risk than less-parsimonious ones.