Hostname: page-component-586b7cd67f-rcrh6 Total loading time: 0 Render date: 2024-11-24T12:56:38.317Z Has data issue: false hasContentIssue false
  • English
  • Français

On Combining Quota-Share and Excess of Loss

Published online by Cambridge University Press:  29 August 2014

Lourdes Centeno
Lourdes Centeno*
Affiliation:
Heriot-Watt University, Edinburgh, Scotland
Rights & Permissions [Opens in a new window]

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.

This paper considers reinsurance retention limits in cases where the cedent has a choice between a pure quota-share treaty, a pure excess of loss treaty or a combination of the two. Our primary aim is to find the combination of retention limits which minimizes the skewness coefficient of the insurer's retained risk subject to constraints on the variance and the expected value of his retained risk. The results are given without specifying precisely how the excess of loss reinsurance premium is calculated. It is also shown that, depending to some extent on the constraint on the variance, the solution to the problem is a pure excess of loss treaty if the excess of loss premium is calculated using the expected value or standard deviation principle but that this need not be true if the variance principle is used.

Keywords

ReinsuranceQuota-shareExcess of lossskewnesscoefficient of variationconstrained optimization
Type
Research Article
Information
ASTIN Bulletin: The Journal of the IAA , Volume 15 , Issue 1 , April 1985 , pp. 49 - 63
Copyright
Copyright © International Actuarial Association 1985

References

Apostol, T. M. (1963) Mathematical Analysis. Addinson-Wesley: London.Google Scholar
Arrow, K. J., and Enthoven, A. C. (1961) Quasi-Concave Programming. Econometrica 29, 779–800.CrossRefGoogle Scholar
Bühlmann, H. (1970) Mathematical Methods in Risk Theory. Springer-Verlag: Berlin, Heidelberg, New York.Google Scholar
Carter, R. L. (1979) Reinsurance. Kluwer Publishing: Great Britain.Google Scholar
Gerathewohl, K. (1980) Reinsurance: Principles and Practice. Verlag Versicherungswirtschaft e. V. Karlsruhe.Google Scholar
Gerber, H. U. (1979) An Introduction to Mathematical Risk Theory. Richard D. Irwin, Inc.: Homewood.Google Scholar
Hadley, G. (1967) Nonlinear and Dynamic Programming. Addison-Wesley: London.Google Scholar
Lemaire, J., Reinhard, J. M. and Vincke, Ph. (1981) A New approach to Reinsurance: Multicriteria Analysis. Net Retentions, 7–42. Nederlandse Reassurantie Groep NV: Amsterdam.Google Scholar