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A collective risk comparative study. (English) Zbl 0602.62095

Infinite time ruin probabilities are computed by the convolution method, the incomplete gamma function method, and an inverse Gaussian method for a real-life example involving data from 24,000 life insurance policies. Some analysis of the methods, and computational suggestions are included.

MSC:

62P05 Applications of statistics to actuarial sciences and financial mathematics

Software:

MACSYMA
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References:

[1] Beekman, J. A., Two Stochastic Processes (1974), Almqvist and Wiksell, Stockholm: Almqvist and Wiksell, Stockholm New York, also Halsted Press (c/o Wiley) · Zbl 0137.35601
[2] Beekman, J. A., A series for infinite time ruin probabilities, Insurance: Mathematics and Economics, 4, 129-134 (1985) · Zbl 0567.62087
[3] Beekman, J. A.; Fuelling, C. P., Risk convolution calculations, Scandinavian Actuarial Journal, 64, 151-164 (1981) · Zbl 0479.62077
[4] Golden, V. E., Introductory MACSYMA Documentation: A Collection of Papers (1983), Laboratory for Computer Science, MIT: Laboratory for Computer Science, MIT Cambridge, MA
[5] MACSYMA Reference Manual, Version 10 (1983), Laboratory for Computer Science, MIT: Laboratory for Computer Science, MIT Cambridge, MA
[6] Rand, R. H., Computer Algebra in Applied Mathematics: An Introduction to MACSYMA (1984), Pitman: Pitman Boston, MA · Zbl 0583.68012
[7] Reckin, G. E.; Schwark, D. J.; Snyder, J. B., Practical applications of the ruin function, Transactions of the Society of Actuaries, 36, 453-477 (1984)
[8] Sloane, N. J.A., My friend MACSYMA, Notices of the American Mathematical Society, 33, 40-43 (1986)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.