Hostname: page-component-cd9895bd7-jkksz Total loading time: 0 Render date: 2024-12-29T13:04:02.898Z Has data issue: false hasContentIssue false
  • English
  • Français

Real-time measurement of portfolio mortality levels in the presence of shocks and reporting delays

Published online by Cambridge University Press:  21 February 2022

Stephen J. Richards Open the ORCID record for Stephen J. Richards [Opens in a new window]
Stephen J. Richards*
Affiliation:
Longevitas Ltd, Edinburgh EH3 6AJ, UK
*
E-mail: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

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.

Keywords

COVID-19Seasonal variationOBNRNowcasting
Type
Original Research Paper
Information
Annals of Actuarial Science , Volume 16 , Issue 3: Special Issue: Managing the risk of mortality shocks , November 2022 , pp. 430 - 452
Copyright
© The Author(s), 2022. Published by Cambridge University Press on behalf of Institute and Faculty of Actuaries

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Akaike, H. (1987). Factor analysis and AIC. Psychometrica, 52, 0 317–333. ISSN 0033–3123. doi: 10.1007/BF02294359.CrossRefGoogle Scholar
Anderson, P.K., Borgan, Ø., Gill, R.D. & Keiding, N. (1992). Statistical Models Based on Counting Processes. Springer, New York. ISBN 0-387-94519-9.Google Scholar
BaŃbura, M., Giannone, D., Modugno, M. & Reichlin, L. (2013). Chapter 4: now-casting and the real-time data flow. In Elliott, G. & Timmermann, A. (Eds.), Handbook of Economic Forecasting (pp. 195–237), vol. 2. Elsevier. doi: 10.1016/B978-0-444-53683-9.00004-9.Google Scholar
Black, D.A., Hsu, Y.-C., Sanders, S.G., Schofield, L.S. & Taylor, L.J. (2017). The Methuselah effect: the pernicious impact of unreported deaths on old-age mortality estimates. Demography, 540 (6), 0 2001–2024. ISSN 00703370, 15337790. doi: 10.2307/45047330.Google Scholar
Butenhof, D.R. (1997). Programming with POSIX Threads. Addison-Wesley, Boston. ISBN 978-0-201-63392-4.Google Scholar
CCAES (2020). Actualización no. 120. Enfermedad por el coronavirus (COVID-19). 29.05.2020, technical report 120, Centro de CoordinaciÓn de Alertas y Emergencias Sanitarias.Google Scholar
Collett, D. (2003). Modelling Survival Data in Medical Research, 2nd edition. Chapman and Hall, Boca Raton. ISBN 1-58488-325-1.Google Scholar
Council of European Union (2016). Regulation (EU) 2016/679. Official Journal of the European Union, 59. ISSN 1977-0677.Google Scholar
Djeundje, V.A.B. & Currie, I.D. (2011). Smoothing dispersed counts with applications to mortality data. Annals of Actuarial Science, 5(I), 0 33–52.CrossRefGoogle Scholar
Dodd, E., Streftaris, G., Waters, H. R. & Stott, A. D. (2015). The effect of model uncertainty on the pricing of critical illness insurance. Annals of Actuarial Science, 9(1), 108–133. doi: 10.1017/S1748499514000244.Google Scholar
Haastrup, S. & Arjas, E. (1996). Claims reserving in continuous time; a nonparametric Bayesian approach. ASTIN Bulletin, 260 (2), 0 139–164. doi: 10.2143/AST.26.2.563216.Google Scholar
Istat (2020). Total deaths per age class, week of demographic event and municipality of residence at the time of death, technical report, Istituto Nazionale di Statistica. Available at https://protect-eu.mimecast.com/s/TgruCAPqquJPK64sn8YmR?domain=istat.it.Google Scholar
Jewell, W.S. (1985). Bayesian extensions to a basic model of software reliability. IEEE Transactions on Software Engineering, SE-110 (12), 0 1465–1471. doi: 10.1109/TSE.1985.231890.Google Scholar
Jewell, W.S. (1989). Predicting IBNYR events and delays: I. continuous time. ASTIN Bulletin, 190 (1), 0 25–55. doi: 10.2143/AST.19.1.2014914.Google Scholar
Kalbfleisch, J.D. & Lawless, J.F. Regression models for right truncated data with applications to AIDS incubation times and reporting lags. Statistica Sinica, 10 (1), 0 19–32. ISSN 10170405, 19968507. Available at https://protect-eu.mimecast.com/s/RZgbCBLoosJkX6jsERxVA?domain=jstor.org, year=1991.Google Scholar
Kaplan, E.L. & Meier, P. (1958). Nonparametric estimation from incomplete observations. Journal of the American Statistical Association, 53, 0 457–481.CrossRefGoogle Scholar
Kreyszig, E. (1999). Advanced Engineering Mathematics, 8th edition. John Wiley and Sons. ISBN 0-471-33328-X.Google Scholar
Lawless, J.F. (1994). Adjustments for reporting delays and the prediction of occurred but not reported events. Canadian Journal of Statistics, 220 (1), 0 15–31. doi: 10.2307/3315826.n1.Google Scholar
Macdonald, A. S., Richards, S. J. & Currie, I. D. (2018). Modelling Mortality with Actuarial Applications. Cambridge University Press, Cambridge. ISBN 978-1-107-04541-5.CrossRefGoogle Scholar
Midthune, D. N., Fay, M. P., Clegg, L. X. & Feuer, E. J. (2005). Modeling Reporting Delays and Reporting Corrections in Cancer Registry Data. Journal of the American Statistical Association, 100(469), 61–70.CrossRefGoogle Scholar
McCullagh, P. & Nelder, J. A. (1989). Generalized Linear Models. Monographs on Statistics and Applied Probability. Chapman and Hall, London. ISBN 0-412-31760-5.Google Scholar
Madrigal, A., Matthews, F., Patel, D., Gaches, A. & Baxter, S. (2011). What longevity predictors should be allowed for when valuing pension scheme liabilities? British Actuarial Journal, 16(1), 1–62. doi: 10.1017/S1357321711000018.Google Scholar
Minister of Justice for Canada. (2018). Personal Information Protection and Electronic Documents Act. S.C. 2000, c. 5.Google Scholar
Richards, S. J. (2020). A {H}ermite-spline model of post-retirement mortality. Scandinavian Actuarial Journal, 2020(2), 110–127. doi: 10.1080/03461238.2019.1642239.CrossRefGoogle Scholar
Richards, S. J., Kaufhold, K. & Rosenbusch, S. (2013). Creating portfolio-specific mortality tables: a case study. European Actuarial Journa, 3(2), 295–319. doi: 10.1007/s13385-013-0076-6.Google Scholar
Richards, S. J., Ramonat, S. J., Vesper, G. & Kleinow, T. (2020). Modelling seasonal mortality with individual data. Scandinavian Actuarial Journal, 1–15. doi: 10.1080/03461238.2020.1777194.Google Scholar
Rau, R. (2007). Seasonality in human mortality: a demographic approach. Demographic Research Monographs 03 XVI. Springer Verlag. ISBN 3-540-44900-0.Google Scholar
Nelson, W. (1958). Theory and applications of hazard plotting for censored failure times. Technometrics, 14, 945–965.Google Scholar
State of California Office of Legislative Counsel (2018). The California Consumer Privacy Act of 2018. Assembly Bill No. 375.Google Scholar
The Novel Coronavirus Pneumonia Emergency Response Epidemiology Team (2020). The epidemiological characteristics of an outbreak of 2019 novel coronavirus diseases (COVID-19) — China, 2020. China CDC Weekly, 2, 0 113. ISSN 2096-7071. Available at https://protect-eu.mimecast.com/s/b1dWCoQRRfp1VqEuOVKXy?domain=weekly.chinacdc.cn.CrossRefGoogle Scholar