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Mis-estimation risk: measurement and impact

Published online by Cambridge University Press:  12 October 2016

S. J. Richards
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Abstract

When deriving a demographic basis from experience data it is useful to know (i) what uncertainty surrounds that basis, and (ii) the financial impact of that uncertainty. Under the Solvency II regime in the EU, insurers must hold capital against a number of risks. One of these is mis-estimation risk, i.e. the uncertainty over the current rates of mortality and other biometric risks experienced by a portfolio. We propose a general method for assessing mis-estimation risk, and by way of illustration we look at how mis-estimation risk can be assessed for a portfolio of pensions in payment from a UK pension scheme. We find that the impact of mis-estimation risk varies according to the risk factors included in a model, and that the inclusion of some necessary risk factors increases the financial impact of mis-estimation risk. In particular, the inclusion of risk factors which improve the model’s fit and financial applicability can lead to an increase in the mis-estimation risk. We also find that a full-portfolio valuation is preferable to using model points when assessing mis-estimation risk.

Keywords

Mis-Estimation RiskParameter RiskSolvency II
Type
Sessional meetings: papers and abstracts of discussions
Information
British Actuarial Journal , Volume 21 , Issue 3 , September 2016 , pp. 429 - 457
Copyright
© Institute and Faculty of Actuaries 2016 

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References

Akaike, H. (1987). Factor analysis and AIC. Psychometrica, 52, 317–333.CrossRefGoogle Scholar
Baker, R.J. & Nelder, J.A. (1978). The GLIM System Release 3 Manual. Oxford: Numerical Algorithms Group.Google Scholar
Cairns, A.J.G., Blake, D. & Dowd, K. (2006). A two-factor model for stochastic mortality with parameter uncertainty: theory and calibration. Journal of Risk and Insurance, 73, 687–718.Google Scholar
CMI Ltd. (2014). Graduations of the CMI SAPS 2004–2011 Mortality Experience Based On Data Collected by 30 June 2012 – Final “S2” Series of Mortality Tables . London: CMI Ltd.Google Scholar
Cox, D.R. & Hinkley, D.V. (1996). Theoretical Statistics. London: Chapman and Hall.Google Scholar
Gompertz, B. (1825). The nature of the function expressive of the law of human mortality. Philosophical Transactions of the Royal Society of London, 115, 513–585.Google Scholar
Hardy, M.R. & Panjer, H.H. (1998). A credibility approach to mortality risk. ASTIN Bulletin, 28(2), 269–283.Google Scholar
Harrell, F.E. & Davis, C.E. (1982). A new distribution-free quantile estimator. Biometrika, 69, 635–640.Google Scholar
Kaplan, E.L. & Meier, P. (1958). Nonparametric estimation from incomplete observations. Journal of the American Statistical Association, 53, 457–481.CrossRefGoogle Scholar
Lindgren, B.W. (1976). Statistical Theory (3rd ed.). London: Collier Macmillan.Google Scholar
Lindley, D.V. & Scott, W.F. (1984). New Cambridge Elementary Statistical Tables. Cambridge: Cambridge University Press.Google Scholar
Longevitas Development Team (2014). Longevitas v2.7.1 User Guide. Edinburgh, United Kingdom: Longevitas Ltd.Google Scholar
Makeham, W.M. (1860). On the law of mortality and the construction of annuity tables. Journal of the Institute of Actuaries and Assurance Magazine, 8, 301–310.Google Scholar
McCullagh, P. & Nelder, J.A. (1989). Generalized Linear Models. Monographs on Statistics and Applied Probability (2nd ed.), vol. 37 London: Chapman and Hall.Google Scholar
Plat, R. (2011). One-year Value-at-Risk for longevity and mortality, Insurance: Mathematics and Economics, Vol. 49(3), 462–470.Google Scholar
R Core Team (2012). R: A Language and Environment for Statistical Computing. Vienna, Austria: R Foundation for Statistical Computing; ISBN 3-900051-07-0.Google Scholar
Richards, S.J. (2008). Applying survival models to pensioner mortality data. British Actuarial Journal, 14(II), 257–326.Google Scholar
Richards, S.J. (2012). A handbook of parametric survival models for actuarial use. Scandinavian Actuarial Journal, 2012(4), 233–257.Google Scholar
Richards, S.J. and Currie, I.D. (2009). Longevitas risk and annuity pricing with the Lee-Carter model, British Actuarial Journal, Vol. 15(II) No. 65, 317–365 (with discussion).Google Scholar
Richards, S.J., Currie, I.D. & Ritchie, G.P. (2014). A value-at-risk framework for longevity trend risk. British Actuarial Journal, 19(1), 116–167.Google Scholar
Richards, S.J., Kaufhold, K. & Rosenbusch, S. (2013). Creating portfolio-specific mortality tables: a case study. European Actuarial Journal, 3(2), 295–319.CrossRefGoogle Scholar
Venables, W.N. & Ripley, B.D. (2002). Modern Applied Statistics with S (4th ed.). New York: Springer.Google Scholar
Wetherill, G.B. (1982). ). Elementary Statistical Methods (3rd ed.). London: Chapman and Hall.Google Scholar
Willets, R.C. (1999). Mortality in the Next Millennium. London: Staple Inn Actuarial Society.Google Scholar