Asymptotic Behaviour of Compound Distributions and Stop-loss Premiums

Bjørn Sundt

doi:10.1017/S0515036100004670

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.

The paper gives some asymptotic results for the compound distribution of aggregate claims when the claim number distribution is negative binomial. The case when the claim numbers are geometrically distributed, is treated separately.

References

REFERENCES

Feller, W. (1971). An Introduction to Probability Theory and its Applications. Vol. II (2nd. ed.): Wiley, New York.Google Scholar

Karlin, S. and Taylor, H. M. (1975). A First Course in Stochastic Processes. Academic Press: New York.Google Scholar

Crossref Citations

This article has been cited by the following publications. This list is generated based on data provided by Crossref.

Teugels, Jozef L. 1985. Approximation and estimation of some compound distributions. Insurance: Mathematics and Economics, Vol. 4, Issue. 3, p. 143.

Embrechts, Paul Maejima, Makoto and Teugels, Jozef L. 1985. Asymptotic Behaviour of Compound Distributions. ASTIN Bulletin, Vol. 15, Issue. 1, p. 45.

Runnenburg, J.Th. and Goovaerts, M.J. 1985. Bounds on compound distributions and stop-loss premiums. Insurance: Mathematics and Economics, Vol. 4, Issue. 4, p. 287.

Jewell, W.S. and Milidiu, R.L. 1986. Strategies for computation of compound distributions with two-sided severities. Insurance: Mathematics and Economics, Vol. 5, Issue. 2, p. 119.

Teugels, J.L. and Willmot, G. 1987. Approximations for stop-loss premiums. Insurance: Mathematics and Economics, Vol. 6, Issue. 3, p. 195.

Omey, E. and Willekens, E. 1987. Theory prob. appl.. Communications in Statistics. Stochastic Models, Vol. 3, Issue. 3, p. 311.

Willmot, Gordon E. 1989. Limiting tail behaviour of some discrete compound distributions. Insurance: Mathematics and Economics, Vol. 8, Issue. 3, p. 175.

Csörgő, Sándor and Teugels, Jef L. 1990. Empirical Laplace transform and approximation of compound distributions. Journal of Applied Probability, Vol. 27, Issue. 1, p. 88.

Sundt, Bjørn 1992. On some Extensions of Panjer's Class of Counting Distributions. ASTIN Bulletin, Vol. 22, Issue. 1, p. 61.

Dhaene, Jan Willmot, Gordon and Sundt, Bjørn 1999. Recursions for Distribution Functions and Stop-Loss Transforms. Scandinavian Actuarial Journal, Vol. 1999, Issue. 1, p. 52.

Willmot, Gordon E. 2002. On higher-order properties of compound geometric distributions. Journal of Applied Probability, Vol. 39, Issue. 2, p. 324.

Willmot, Gordon E. 2002. On higher-order properties of compound geometric distributions. Journal of Applied Probability, Vol. 39, Issue. 02, p. 324.

Cai, Jun 2004. Encyclopedia of Actuarial Science.

Mircea, Iulian and Covrig, Mihaela 2010. Some Methods Used in the Estimation of the Ruin Probability. p. 319.

Cai, Jun 2014. Wiley StatsRef: Statistics Reference Online.

Badía, F. G. and Sangüesa, C. 2015. Inventory models with nonlinear shortage costs and stochastic lead times; applications of shape properties of randomly stopped counting processes. Naval Research Logistics (NRL), Vol. 62, Issue. 5, p. 345.

Jin, Tao Provost, Serge B. and Ren, Jiandong 2016. Moment-based density approximations for aggregate losses. Scandinavian Actuarial Journal, Vol. 2016, Issue. 3, p. 216.

Giuricich, Mario and Burnecki, Krzysztof 2017. Stable Weak Approximation at Work in Index-Linked Catastrophe Bond Pricing. SSRN Electronic Journal ,

Burnecki, Krzysztof and Giuricich, Mario 2017. Stable Weak Approximation at Work in Index-Linked Catastrophe Bond Pricing. Risks, Vol. 5, Issue. 4, p. 64.

Download full list

Article contents

Asymptotic Behaviour of Compound Distributions and Stop-loss Premiums

Abstract

References

REFERENCES

Save article to Kindle

Save article to Dropbox

Save article to Google Drive

Reply to: Submit a response

Your details

You have entered the maximum number of contributors

Conflicting interests