Using WinBUGS to Study Family Frailty in Child Mortality, with an Application to Child Survival in Ivory Coast

This article analyzes the effects of unobserved family heterogeneity in children survival times through a Bayesian approach. We rely on survey data from Ivory Coast and use a proportional hazard model with multiplicative random effect. With such a model, the usual assumption of independence of observations is avoided. The posterior distributions of the parameters are estimated through a Gibbs sampler algorithm using the WinBUGS software. This technique overcomes the possible local convergence problem observed with the commonly used Expectation-Maximization method

Still living with mortality: The longevity risk transfer market after one decade

This paper updates Living with Mortality published in 2006. It describes how the longevity risk transfer market has developed over the intervening period, and, in particular, how insurance-based solutions – buy-outs, buy-ins and longevity insurance – have triumphed over capital markets solutions that were expected to dominate at the time. Some capital markets solutions – longevity-spread bonds, longevity swaps, q-forwards, and tail-risk protection – have come to market, but the volume of business has been disappointingly low. The reason for this is that when market participants compare the index-based solutions of the capital markets with the customized solutions of insurance companies in terms of basis risk, credit risk, regulatory capital, collateral, and liquidity, the former perform on balance less favourably despite a lower potential cost.We discuss the importance of stochastic mortality models for forecasting future longevity and examine some applications of these models, e.g., determining the longevity risk premiumand estimating regulatory capital relief. The longevity risk transfer market is now beginning to recognize that there is insufficient capacity in the insurance and reinsurance industries to deal fully with demand and new solutions for attracting capital markets investors are now being examined – such as longevity-linked securities and reinsurance sidecars

Modelling Mortality for Pension Schemes

For many pension schemes, a shortage of data limits their ability to use sophisticated stochastic mortality models to assess and manage their exposure to longevity risk. In this study, we develop a mortality model designed for such pension schemes, which compares the evolution of mortality rates in a sub-population with that observed in a larger reference population. We apply this approach to data from the CMI Self-Administered Pension Scheme study, using U.K. population data as a reference. We then use the approach to investigate the potential differences in the evolution of mortality rates between these two populations and find that, in many practical situations, basis risk is much less of a problem than is commonly believed

Modelling and forecasting mortality in Spain

[EN] Experience shows that static life tables overestimate death probabilities. As a consequence of this overestimation the premiums for annuities, pensions and life insurance are not what they actually should be, with negative effects for insurance companies or policy-holders. The reason for this overestimation is that static life tables, through being computed for a specific period of time, cannot take into account the decreasing mortality trend over time. Dynamic life tables overcome this problem by incorporating the influence of the calendar when graduating mortality. Recent papers on the topic look for the development of new methods to deal with this dynamism. Most methods used in dynamic tables are parametric, apply traditional mortality laws and then analyse the evolution of estimated parameters with time series techniques. Our contribution consists in extending and applying Lee–Carter methods to Spanish mortality data, exploring residuals and future trends.This work was partially supported by a grant from MEyC (Ministerio de Educacio´n y Ciencia, Spain, project MTM-2004-06231). The research of Francisco Montes has also been partially supported by a grant from DGITT (Direccio´ General d’Investigacio´ i Transfere`ncia Tecnolo`gica de la Generalitat Valenciana, project GRUPOS03/189).Debón Aucejo, AM.; Montes, F.; Puig, F. (2008). Modelling and forecasting mortality in Spain. European Journal of Operational Research. 189(3):624-637. https://doi.org/10.1016/j.ejor.2006.07.050S624637189

Bridging the age gap: a prognostic model that predicts survival and aids in primary treatment decisions for older women with oestrogen receptor‐positive early breast cancer

Background A prognostic model was developed and validated using cancer registry data. This underpins an online decision support tool, informing primary treatment choice for women aged 70 years or older with hormone receptor‐positive early breast cancer. Methods Data from women diagnosed between 2002 and 2010 in the English Northern and Yorkshire and West Midlands regions were used to develop the model. Primary treatment options of surgery with adjuvant endocrine therapy or primary endocrine therapy were compared. Models predicting the hazard of breast cancer‐specific mortality and hazard of other‐cause mortality were combined to derive survival probabilities. The model was validated externally using data from the Eastern Cancer Registration and Information Centre. Results The model was developed using data from 23 842 women, and validated externally on a data set from 14 526 patients. The overall model calibration was good. At 2 and 5 years, predicted mortality from breast cancer and other causes differed from the observed rate by less than 1 per cent. At 5 years, there were slight overpredictions in breast cancer mortality (2629 predicted versus 2556 observed deaths; P  = 0·142) and mortality from all causes (6399 versus 6320 respectively; P  = 0·583). The discrepancy varied between subgroups. Model discrimination was 0·75 or above for all mortality measures. Conclusion A prognostic model for older women with oestrogen receptor‐positive early breast cancer was developed and validated in the present study. This forms a basis for an online decision support tool (https://agegap.shef.ac.uk/)

A parameterized approach to modeling and forecasting mortality

A new method is proposed of constructing mortality forecasts. This parameterized approach utilizes Generalized Linear Models (GLMs), based on heteroscedastic Poisson (non-additive) error structures, and using an orthonormal polynomial design matrix. Principal Component (PC) analysis is then applied to the cross-sectional fitted parameters. The produced model can be viewed either as a one-factor parameterized model where the time series are the fitted parameters, or as a principal component model, namely a log-bilinear hierarchical statistical association model of Goodman [Goodman, L.A., 1991. Measures, models, and graphical displays in the analysis of cross-classified data. J. Amer. Statist. Assoc. 86(416), 1085–1111] or equivalently as a generalized Lee–Carter model with p interaction terms. Mortality forecasts are obtained by applying dynamic linear regression models to the PCs. Two applications are presented: Sweden (1751–2006) and Greece (1957–2006)

Modelling longevity bonds: Analysing the Swiss Re Kortis bond

A key contribution to the development of the traded market for longevity risk was the issuance of the Kortis bond, the world's first longevity trend bond, by Swiss Re in 2010. We analyse the design of the Kortis bond, develop suitable mortality models to analyse its payoff and discuss the key risk factors for the bond. We also investigate how the design of the Kortis bond can be adapted and extended to further develop the market for longevity risk

Computational framework for longevity risk management

Longevity risk threatens the financial stability of private and government sponsored defined benefit pension systems as well as social security schemes, in an environment already characterized by persistent low interest rates and heightened financial uncertainty. The mortality experience of countries in the industrialized world would suggest a substantial age-time interaction, with the two dominant trends affecting different age groups at different times. From a statistical point of view, this indicates a dependence structure. It is observed that mortality improvements are similar for individuals of contiguous ages (Wills and Sherris, Integrating financial and demographic longevity risk models: an Australian model for financial applications, Discussion Paper PI-0817, 2008). Moreover, considering the dataset by single ages, the correlations between the residuals for adjacent age groups tend to be high (as noted in Denton et al., J Population Econ 18:203-227, 2005). This suggests that there is value in exploring the dependence structure, also across time, in other words the inter-period correlation. In this research, we focus on the projections of mortality rates, contravening the most commonly encountered dependence property which is the "lack of dependence" (Denuit et al., Actuarial theory for dependent risks: measures. Orders and models, Wiley, New York, 2005). By taking into account the presence of dependence across age and time which leads to systematic over-estimation or under-estimation of uncertainty in the estimates (Liu and Braun, J Probability Stat, 813583:15, 2010), the paper analyzes a tailor-made bootstrap methodology for capturing the spatial dependence in deriving confidence intervals for mortality projection rates. We propose a method which leads to a prudent measure of longevity risk, avoiding the structural incompleteness of the ordinary simulation bootstrap methodology which involves the assumption of independence

A comparative study of two population models for the assessment of basis risk in longevity hedges

Longevity swaps have been one of the major success stories of pension scheme derisking in recent years. However, with some few exceptions, all of the transactions to date have been bespoke longevity swaps based upon the mortality experience of a portfolio of named lives. In order for this market to start to meet its true potential, solutions will ultimately be needed that provide protection for all types of members, are cost effective for large and smaller schemes, are tradable, and enable access to the wider capital markets. Index-based solutions have the potential to meet this need; however concerns remain with these solutions. In particular, the basis risk emerging from the potential mismatch between the underlying forces of mortality for the index reference portfolio and the pension fund/annuity book being hedged is the principal issue that has, to date, prevented many schemes progressing their consideration of index-based solutions. Two-population stochastic mortality models offer an alternative to overcome this obstacle as they allow market participants to compare and project the mortality experience for the reference and target populations and thus assess the amount of demographic basis risk involved in an index-based longevity hedge. In this paper, we systematically assess the suitability of several multi-population stochastic mortality models for assessing basis risks and provide guidelines on how to use these models in practical situations paying particular attention to the data requirements for the appropriate calibration and forecasting of such models