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Weighted Mortality Rates as Early Warning Signals for Insurance Companies

Published online by Cambridge University Press:  29 August 2014

Leigh A. Roberts
Leigh A. Roberts*
Affiliation:
Institute of Statistics and Operations Research, Victoria University, Wellington, New Zealand
*
Institute of Statistics and Operations Research, Victoria University of Wellington, P.O. Box 600, Wellington, New Zealand
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Abstract

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Weighted mortality rates are commonly used in actuarial work, but the inter-relationship between the weights used and the underlying mortality rates seems not to have been widely investigated.

Calculation of the ratio of weighted mortality rates to conventional mortality rates provides a simple means for an insurance company to track changes in the underlying mortality of its portfolio over time, and acts as an early warning system for possible deterioration of underwriting results. Asymptotic distributions are found for this ratio, and for the mortality rates themselves. It is suggested that insurance companies commence to gather data for the calculation of this ratio for the insurance sector as a whole, for the main annuity and assurance classes.

Keywords

Asymptotic distributiondecremental ratesearly warning signalsinsuranceratio of weighted to unweighted mortality ratessums at riskunderlying mortality trendsweighted mortality rates
Type
Workshop
Information
ASTIN Bulletin: The Journal of the IAA , Volume 23 , Issue 2 , November 1993 , pp. 273 - 286
Copyright
Copyright © International Actuarial Association 1993

References

REFERENCES

Batten, R.W. (1978) Mortality Table Construction. Prentice-Hall.Google Scholar
CMIR1 (1973) Continuous Mortality Investigation Report No. 1. Continuous Mortality Investigation Bureau. Institute of Actuaries, Faculty of Actuaries.Google Scholar
CMIR2 (1976) Continuous Mortality Investigation Report No. 2. Continuous Mortality Investigation Bureau. Institute of Actuaries, Faculty of Actuaries.Google Scholar
CMIR3 (1978) Continuous Mortality Investigation Report No. 3. Continuous Mortality Investigation Bureau. Institute of Actuaries, Faculty of Actuaries.Google Scholar
CMIR6 (1983) Continuous Mortality Investigation Report No. 6. Continuous Mortality Investigation Bureau. Institute of Actuaries, Faculty of Actuaries.Google Scholar
Cody, D.C. (1941) Actuarial note: the standard deviation in the rate of mortality by amounts. Transactions, Actuarial Society of America 42, (1) 69–73.Google Scholar
Cox, P. R. (1976) Demography. 5th edition. Cambridge University Press.CrossRefGoogle Scholar
Elandt-Johnson, R. C. and Johnson, N. L. (1980) Survival Models and Data Analysis. Wiley.Google Scholar
Haberman, S. (1988) Measuring relative mortality experience. Jnl. of the Institute of Actuaries 115, (II) 271–298.CrossRefGoogle Scholar
ISC (1992) Insurance and Superannuation Commission Annual Report 1991-1992. Australian Government Publication.Google Scholar
Kitagawa, E. M. (1964) Standardised comparisons in population research. Demography 1, 296–315.CrossRefGoogle Scholar
Klugman, S.A. (1981) On the variance and mean squared error of decrement estimators. Trans., Soc. of Actuaries 33, 301–311.Google Scholar
Pollard, A.H. (1970) Random mortality fluctuations and the binomial hypothesis. Jnl. of the Institute of Actuaries 96, (II) 251–264.CrossRefGoogle Scholar
Rao, C. R. (1973) Linear statistical inference and its applications. Second edition. Wiley.CrossRefGoogle Scholar
Roberts, L. A. (1992a) Exact Moments and Asymptotic Distributions of Weighted Mortality Rates. Technical Report No. 23, Institute of Statistics and Operations Research, Victoria University, Wellington.Google Scholar
Roberts, L. A. (1992b) On ratios of random variables and generalised mortality rates. Jnl. Applied Probability 29, (2) 268–279.CrossRefGoogle Scholar
SocActs (1987) 1985, 1986 and 1987 reports of mortality, morbidity and other experience. Trans., Soc. of Actuaries, 35–69.Google Scholar