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Limiting Distribution of the Present Value of a Portfolio

Published online by Cambridge University Press:  29 August 2014

Gary Parker
Gary Parker*
Affiliation:
Simon Fraser University
*
Department of Mathematics and Statistics, Simon Fraser University, Burnaby, BC V5A 1S6, Canada.
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Abstract

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An approximation of the distribution of the present value of the benefits of a portfolio of temporary insurance contracts is suggested for the case where the size of the portfolio tends to infinity. The model used is the one presented in Parker (1922b) and involves random interest rates and future lifetimes. Some justifications of the approximation are given. Illustrations for limiting portfolios of temporary insurance contracts are presented for an assumed Ornstein-Uhlenbeck process for the force of interest.

Keywords

Force of interestOrnstein-Uhlenbeck processPortfolio of policiesPresent value functionLimiting distribution
Type
Articles
Information
ASTIN Bulletin: The Journal of the IAA , Volume 24 , Issue 1 , May 1994 , pp. 47 - 60
Copyright
Copyright © International Actuarial Association 1994

References

REFERENCES

Beekman, J.A. and Fuelling, C.P. (1990) Interest and Mortality Randomness in Some Annuities. Insurance: Mathematics and Economics 9, 185–196.Google Scholar
Boyle, P.P. (1976) Rates of Return as Random Variables. JRI XLIII, 693–713.Google Scholar
Chung, K.L. (1974) A Course in Probability Theory. Second edition, 365 pp., Academic Press, New York.Google Scholar
Coward, L. E. (1988) Mercer Handbook of Canadian Pension and Welfare Plans. 9th edition, 337 pp., CCH Canadian, Don Mills.Google Scholar
Devolder, P (1986) Opérations Stochastiques de Capitalisation. ASTIN Bulletin 16S, S5–S30.CrossRefGoogle Scholar
Dhaene, J. (1989) Stochastic Interest Rates and Autoregressive Integrated Moving Average Processes. ASTIN Bulletin 19, 131–138.CrossRefGoogle Scholar
Dufresne, D. (1988) Moments of Pension Contributions and Fund Levels when Rates of Return are Random. Journal of the Institute of Actuaries 115, part III, 535–544.CrossRefGoogle Scholar
Dufresne, D. (1990) The Distribution of a Perpetuity, with Applications to Risk Theory and Pension funding. Scandinavian Actuarial Journal, 39–79.CrossRefGoogle Scholar
Frees, E. W. (1990) Stochastic Life Contingencies with Solvency Considerations. Transaction of the Society of Actuaries XLII, 91–148.Google Scholar
Giacotto, C. (1986) Stochastic Modelling of Interest Rates: Actuarial vs. Equilibrium Approach. Journal of Risk and Insurance 53, 435–453.CrossRefGoogle Scholar
Mardia, K. V., Kent, J.T. and Bibby, J.M. (1979) Multivariate Analysis, 463 pp., Academic Press, London.Google Scholar
Melsa, J. L. and Sage, A. P. (1973) An Introduction to Probability and Stochastic Processes, 403 pp., Prentice-Hall, New Jersey.Google Scholar
Morrison, D.F. (1990) Multivariate Statistical Methods. 3rd edition, 586 pp., McGraw-Hill Inc, New York.Google Scholar
Panjer, H. H. and Bellhouse, D. R. (1980) Stochastic Modelling of Interest Rates and Applications to Life Contingencies. Journal of Risk and Insurance 47, 91–110.CrossRefGoogle Scholar
Parker, G. (1992a) An Application of Stochastic Interest Rates Models in Life Assurance, 229 pp., Ph.D. thesis, Heriot-Watt University.Google Scholar
Parker, G. (1992b) Moments of the present value of a portfolio of policies. To appear in Scandinavian Actuarial Journal.Google Scholar
Ross, S. (1988) A First Course in Probability. 3rd edition, 420 pp., MacMillan, New York.Google Scholar
Waters, H. R. (1978) The Moments and Distributions of Actuarial Functions. Journal of the Institute of Actuaries 105, Part 1, 61–75.CrossRefGoogle Scholar
Wilkie, A. D. (1976) The Rate of Interest as a Stochastic Process-Theory and Applications. Proc. 20th International Congress of Actuaries, Tokyo 1, 325–338.Google Scholar