Hostname: page-component-586b7cd67f-dsjbd Total loading time: 0 Render date: 2024-11-26T17:50:41.670Z Has data issue: false hasContentIssue false
  • English
  • Français

A portfolio of endowment policies and its limiting distribution

Published online by Cambridge University Press:  29 August 2014

Gary Parker
Gary Parker*
Affiliation:
Simon Fraser University, Vancouver
*
Department of Mathematics and Statistics, Simon Fraser University, Burnaby, BC V5A 1S6, Canada
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Two methods for approximating the limiting distribution of the present value of the benefits of a portfolio of identical endowment insurance contracts are suggested. The model used assumes that both future lifetimes and interest rates are random. The first method is similar to the one presented in Parker (1994b). The second method is based on the relationship between temporary and endowment insurance contracts.

Keywords

Force of interestWhite Noise processOrnstein-Uhlenbeck processPortfolio of policiesPresent value functionLimiting distribution
Type
Articles
Information
ASTIN Bulletin: The Journal of the IAA , Volume 26 , Issue 1 , May 1996 , pp. 25 - 33
Copyright
Copyright © International Actuarial Association 1996

References

REFERENCES

Beekman, J.A. and Fuelling, C.P. (1991) Extra randomness in certain annuity models. Insurance: Mathematics and Economics, 10, 275–287.Google Scholar
Beekman, J.A. and Fuelling, C.P. (1993) One approach to dual randomness in life insurance. Scandinavian Actuarial Journal 1993, 2, 173–182.Google Scholar
Coward, L. E. (1988) Mercer handbook of Canadian pension and welfare plans. 9th edition, CCH Canadian, Don Mills, 337 pp.Google Scholar
Frees, E. W. (1990) Stochastic life contingencies with solvency considerations. Transaction of the Society of Actuaries XLII, 91–148.Google Scholar
Mardia, K. V., Kent, J.T. and Bibby, J.M. (1979) Multivariate analysis. Academic Press, London, 463 pp.Google Scholar
Melsa, J. L. and Sage, A. P. (1973) An introduction to probability and stochastic processes. Prentice-Hall, New Jersey, 403 pp.Google Scholar
Norberg, R. (1993) Solvency study in life insurance. Proceedings of the 3th AFIR International Colloquium, 821–830.Google Scholar
Norberg, R. and Møller, C.M. (1993) Thiele's differential equation by stochastic interest of diffusion type. Working paper No 117, Laboratory of Actuarial Mathematics, University of Copenhagen.Google Scholar
Parker, G. (1992) An application of stochastic interest rates models in life assurance. Ph.D. thesis, Heriot-Watt University, 229 pp.Google Scholar
Parker, G. (1994a) Moments of the present value of a portfolio of policies. Scandinavian Actuarial Journal, 1994/1, 53–67.CrossRefGoogle Scholar
Parker, G. (1994b) Limiting distribution of the present value of a portfolio. ASTIN Bulletin, 24/1, 47–60.CrossRefGoogle Scholar
Parker, G. (1994c) Stochastic analysis of an insurance portfolio. Proceedings of the 4th AFIR Colloquium, 49–65.Google Scholar
Parker, G. (1994d) Stochastic analysis of a portfolio of endowment policies. Scandinavian Actuarial Journal, 1994/2, 119–130.CrossRefGoogle Scholar
Parker, G. (1994e) Two stochastic approaches for discounting actuarial functions. ASTIN Bulletin, 24/2, 167–181.CrossRefGoogle Scholar
Parker, G. (1994f) A portfolio of endowment policies and its limiting distribution. Working paper 119, Laboratory of Actuarial Mathematics, University of Copenhagen.Google Scholar