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Improving Goovaerts' and De Vylder's Stable Recursive Algorithm

Published online by Cambridge University Press:  29 August 2014

Colin M. Ramsay
Colin M. Ramsay*
Affiliation:
University of Nebraska-Lincoln
*
Actuarial Science, 310 Burnett Hall, University of Nebraska-Lincoln, Lincoln, NE 68588-0307, U.S.A.
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Abstract

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Goovaerts and de Vylder (1983) provided a stable recursive algorithm for calculating the probability of ultimate ruin. Their algorithm yielded bounds for this probability. It is shown that in practice their method may be inherently unstable because it is based on the subtraction of nearly equal numbers. An alternative to this type of subtraction is provided. It is proved that their algorithm converges only at a linear rate to the true value. It is suggested that this slow rate of convergence be improved via an application of the Richardson extrapolation technique.

Keywords

Ruin probabilityrounding errorstruncation errorsorder of convergenceRichardson extrapolation
Type
Articles
Information
ASTIN Bulletin: The Journal of the IAA , Volume 22 , Issue 1 , May 1992 , pp. 51 - 59
Copyright
Copyright © International Actuarial Association 1992

References

REFERENCES

Abramowitz, M. and Stegun, I. A. (1972) Handbook of Mathematical Functions, 9th edition. Dover Publications, New York.Google Scholar
Baker, C. T. H. (1977) The Numerical Treatment of Integral Equations. Clarendo Press, Oxford.Google Scholar
Brunner, H. and van der Houwen, P. J. (1986) The Numerical Solution of Volterra Equations. North Holland, Amsterdam.Google Scholar
Delves, L. M. and Mohamed, J. L. (1985) Computational Methods for Integral Equations. University Press, Cambridge.CrossRefGoogle Scholar
Gerber, H. U. (1979) An Introduction to Mathematical Risk Theory. Huebner Foundation Monograph, University of Pennsylvania, Philadelphia.Google Scholar
Goovaerts, M. and De Vylder, F. (1983) A Stable Recursive Algorithm for Evaluation of Ultimate Ruin Probabilities. ASTIN Bulletin 14, 53–59.CrossRefGoogle Scholar
Ralston, A. and Rabinowitz, P. (1978) A first Course in Numerical Analysis, 2nd edition. International Student Edition, McGraw-Hill, Japan.Google Scholar
Thorin, O. and Wikstad, N. (1977) Calculation of ruin probabilities when the claim distribution is lognormal. ASTIN Bulletin 9, 231–246.CrossRefGoogle Scholar
Wilkinson, J. H. (1963) Rounding Errors in Algebra Processes. Prentice-Hall, New Jersey.Google Scholar