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A Reserve Basis for Maturity Guarantees in Unit-Linked Life Assurance

Published online by Cambridge University Press:  03 October 2014

W. F. Scott
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Synopsis

The main purpose of this paper is the determination of a basis for the calculation of “prudent” reserves for maturity guarantees in annual and single premium unit-linked life assurance policies, particularly those in which the investment medium is a broad range of U.K. equities. Estimates of the proceeds of equity investments required, and theories of stock market movements are discussed; it is concluded that yearly growth rates, including reinvested net income, may be represented approximately by the lognormal distribution and that yearly growth rates are not random, but negatively correlated. A mathematical model is then developed; the evaluation of the resulting distributions, which is a problem of some interest in its own right in the annual premium case, is discussed in the Appendix. There is a general discussion of certain valuation principles, and we give tables showing the level of reserves suggested by our methods. Various practical questions, such as the treatment of the assets and the effects on reserves of mortality, withdrawals, capital gains tax, policies with different terms and existing business, are also considered.

Type
Research Article
Information
Transactions of the Faculty of Actuaries , Volume 35 , 1975 , pp. 365 - 415
Copyright
Copyright © Institute and Faculty of Actuaries 1975

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References

1.Grant, A. T. and Kingsnorth, G. A.. Unit Trusts and Equity-Linked Endowment Assurances. T.F.A. 30, p. 17 and J.I.A., 93, p. 387.Google Scholar
2.Fine, A. E. M.. Unit-Linked Assurance: Category B. J.I.A., 102, p. 35.Google Scholar
3.Benjamin, S.. Maturity Guarantees for Equity-Linked Policies. Proc. XXth International Congress of Actuaries, Tokyo, 1976.Google Scholar
4.Aitchison, J. and Brown, J. H. C.. The Lognormal Distribution, C.U.P.Google Scholar
5.Cramer, H.. Mathematical Methods of Statistics, Princeton.Google Scholar
6.Wilkie, A. D.. The Rate of Interest as a Stochastic Process—Theory and Applications. Proc. XXth International Congress of Actuaries, Tokyo, 1976.Google Scholar
7.Kahn, P. M.. Projections of Variable Life Insurance Operations. T.S.A., 23, p. 335.Google Scholar
8.Kendall, M. and Stuart, A.. The Advanced Theory of Statistics, vol. 3, third edition, Griffin.Google Scholar
9.Squires, R. J.. Unit-Linked Assurance: Observations and Propositions. J.I.A., 101, p. 1.Google Scholar
10.Discussion on the Report of the Committee on Property Bonds and Equity-Linked Life Assurance. T.F.A., 34, p. 23.Google Scholar
11.Quensel, C.-E.. Studies in the Logarithmic Normal Curve. Skand. Akt., 23, p. 141.Google Scholar
12.Boyle, P. P.. An Approximation Method to Calculate the Value of a Maturity Guarantee under a Level Premium Equity Based Contract. A.R.C.H., Providence, R.I.CrossRefGoogle Scholar
13.Box, G. E. P. and Muller, M. E.. A Note on the Generation of Random Normal Deviates. Ann. Math. Stat., 29, p. 610.Google Scholar