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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

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