Hostname: page-component-cd9895bd7-mkpzs Total loading time: 0 Render date: 2024-12-26T14:01:24.123Z Has data issue: false hasContentIssue false
  • English
  • Français

Two Stochastic Approaches for Discounting Actuarial Functions

Published online by Cambridge University Press:  29 August 2014

Gary Parker
Gary Parker*
Affiliation:
Simon Fraser University
*
Dept. of Mathematics and Statistics, Simon Fraser University, Burnaby, B.C.CanadaV5A 1S6.
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 approaches used to model interest randomness are presented. They are the modeling of the force of interest accumulation function and the modeling of the force of interest. The expected value, standard deviation and coefficient of skewness of the present value of annuities-immediate are presented as illustrations. The implicit behavior of the force of interest under the two approaches is investigated by looking at a particular conditional expectation of the force of interest accumulation function.

Keywords

Force of interestForce of interest accumulation functionWhite Noise processWiener processOrnstein-Uhlenbeck processPresent value functionAnnuity-immediate
Type
Articles
Information
ASTIN Bulletin: The Journal of the IAA , Volume 24 , Issue 2 , November 1994 , pp. 167 - 181
Copyright
Copyright © International Actuarial Association 1994

References

Aitchison, J. and Brown, J.A.C. (1963) The Lognormal Distribution, 176 pp., Cambridge University Press.Google Scholar
Arnold, L. (1974) Stochastic Differential Equations: Theory and Applications, 228 pp., John Wiley & Sons, New York.Google Scholar
Beekman, J. A. and Fuelling, C.P. (1990) Interest and Mortality Randomness in Some Annuities. Insurance: Mathematics and Economics 9, 185–196.Google Scholar
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. To appear.Google Scholar
Bühlmann, H. (1992) Stochastic Discounting. Insurance: Mathematics and Economics 11, 113–127.Google Scholar
Canadian Institute of Actuaries (1993) Rapport sur les Statistiques Économiques Canadiennes, 1924–1992.Google Scholar
De Schepper, A., De Vylder, F., Goovaerts, M. and Kaas, R. (1992a) Interest Randomness in Annuities Certain. Insurance: Mathematics and Economics 11, 271–281.Google Scholar
De Schepper, A., Goovaerts, M. and Delbaen, F. (1992b) The Laplace Transform of Annuities Certain with Exponential Time Distribution. Insurance: Mathematics and Economics 11, 291–294.Google Scholar
De Schepper, A. and Goovaerts, M. (1992) Some Further Results on Annuities Certain with Random Interest. Insurance: Mathematics and Economics 11, 283–290.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. (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
Karlin, S. and Taylor, H. M. (1981) A Second Course in Stochastic Processes, 542 pp., Academic Press, San Diego.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
Mood, A.M., Graybill, F.A. and Boes, D.C. (1974) Introduction to the Theory of Statistics, 567 pp., McGraw-Hill.Google Scholar
Norberg, R. (1993) A Solvency Study in Life Insurance. Proceedings of the 3rd AFIR International Colloquium, 821–830.Google Scholar
Pandit, S.M. and Wu, S.M. (1983) Time Series and System Analysis with Applications, 586 pp., John Wiley & Sons, New York.Google Scholar
Panjer, H.H. and Bellhouse, D. R. (1980) Stochastic Modelling of Interest Rates with Applications to Life Contingencies. Journal of Risk and Insurance 47, 91–110.CrossRefGoogle Scholar
Papachristou, D.J. and Waters, H. R. (1991) Some Remarks Concerning Stochastic Interest Rates in Relation to Long Term Insurance Policies. Scandinavian Actuarial Journal, 103–117.CrossRefGoogle Scholar
Parker, G. (1992) An Application of Stochastic Interest Rates Models in Life Assurance. Ph.D. thesis, Heriot-Watt University.Google Scholar
Parker, G. (1993a) Distribution of the present value of future cash flows. Proceedings of the 3rd AFIR International Colloquium, 831–843.Google Scholar
Parker, G. (1993b) Moments of the present value of a portfolio of policies. To appear in Scandinavian Actuarial Journal.Google Scholar
Parker, G., (1993c) Two Stochastic Approaches for Discounting Actuarial Functions. Proceedings of the XXIV ASTIN Colloquium, 367–389.Google Scholar
Parker, G. (1994) Limiting distribution of the present value of a portfolio. ASTIN Bulletin 94–1, 47–60.CrossRefGoogle 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
Waters, H.R. (1990) The Recursive Calculation of the Moments of the Profit on a Sickness Insurance Policy. Insurance: Mathematics and Economics 9, 101–113.Google Scholar