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A property of the generalized inverse Gaussian distribution with some applications

Published online by Cambridge University Press:  14 July 2016

Paul Embrechts
Paul Embrechts*
Affiliation:
University of Leuven
*
∗ Postal address: Departement Wiskunde K. U. Leuven, Celestijnenlaan 200B, B-3030 Leuven (Heverlee), Belgium.
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Abstract

An asymptotic convolution property for the generalized inverse Gaussian distribution with λ < 0 is proved. This result is applied to calculate the probability of ruin in the general risk model when these distributions are used to model claim sizes. Some related applications are discussed.

Keywords

GENERALIZED INVERSE GAUSSIANRISK THEORYRUIN PROBABILITYSUBEXPONENTIALITY
Type
Research Papers
Information
Journal of Applied Probability , Volume 20 , Issue 3 , September 1983 , pp. 537 - 544
Copyright
Copyright © Applied Probability Trust 1983 

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Footnotes

Research carried out while the author was visiting Imperial College, London with financial support from the Royal Society.

References

Atkinson, A. C. (1979) The simulation of generalized inverse Gaussian, generalized hyperbolic, gamma and related random variables. Research Report No. 52, Department of Theoretical Statistics, Aarhus University.Google Scholar
Barlow, R. E. and Proschan, F. (1965) Mathematical Theory of Reliability. Wiley, New York.Google Scholar
Barndorff-Nielsen, O., Blaesild, P. and Halgreen, C. (1978) First hitting time models for the generalized inverse Gaussian distribution. Stoch. Proc. Appl. 7, 49–54.Google Scholar
Blaesild, P. (1978) The shape of generalized inverse Gaussian and hyperbolic distributions. Research Report No. 37, Department of Theoretical Statistics, Aarhus University.Google Scholar
Chhikara, R. S. and Folks, J. L. (1977) The inverse Gaussian distribution as a lifetime model. Technometrics 19, 461–468.CrossRefGoogle Scholar
Chover, J., Ney, P. and Wainger, S. (1973) Degeneracy properties of subcriticai branching processes. Ann. Prob. 1, 663–673.Google Scholar
Embrechts, P. and Goldie, C. M. (1982) On convolution tails. Stoch. Proc. Appl. 13, 263–278.Google Scholar
Embrechts, P., Goldie, C. M. and Veraverbeke, N. (1979) Subexponentiality and infinite divisibility. Z. Wahrscheinlichkeitsth. 49, 335–347.CrossRefGoogle Scholar
Embrechts, P. and Veraverbeke, N. (1982) Estimates for the probability of ruin with special emphasis on the possibility of large claims. Insurance Math. Econ. 1, 55–72.Google Scholar
Feller, W. (1971) An Introduction to Probability Theory and its Applications, Vol. II, 2nd edn. Wiley, New York.Google Scholar
Goldie, C. M. (1978) Subexponential distributions and dominated-variation tails. J. Appl. Prob. 15, 440–442.Google Scholar
Jørgensen, B. (1982) Statistical Properties of the Generalized Inverse Gaussian Distribution. Lecture Notes in Statistics 9, Springer-Verlag, New York.Google Scholar
Teugels, J. L. (1975) The class of subexponential distribution. Ann. Prob. 3, 1000–1011.CrossRefGoogle Scholar