Hostname: page-component-586b7cd67f-dsjbd Total loading time: 0 Render date: 2024-11-23T22:59:14.676Z Has data issue: false hasContentIssue false
  • English
  • Français

Relative Reinsurance Retention Levels

Published online by Cambridge University Press:  29 August 2014

David C.M. Dickson  and
Howard R. Waters
David C.M. Dickson
Affiliation:
Centre for Actuarial Studies, Faculty of Economics and Commerce, University of Melbourne, Victoria 3052, Australiae-mail:[email protected]
Howard R. Waters
Affiliation:
Department of Actuarial Mathematics and Statistics, Heriot-Watt University, Midlothian EH14 4AS, Great Britain, e-mail:[email protected]
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.

The problem of determining optimal retention levels for a non-life portfolio consisting of a number of independent sub-portfolios was first discussed by de Finetti (1940). He considered retention levels as optimal if they minimised the variance of the insurer's profit from the portfolio subject to the constraint of a fixed level of expected profit. In this paper we consider a similar problem, changing the criterion for optimality to minimising the probability of ruin, either in discrete or continuous time. We investigate this problem through a series of case studies based on a real portfolio.

Keywords

Reinsuranceoptimal retention levelsfinite time ruintranslated gamma process
Type
Articles
Information
ASTIN Bulletin: The Journal of the IAA , Volume 27 , Issue 2 , November 1997 , pp. 207 - 227
Copyright
Copyright © International Actuarial Association 1997

References

REFERENCES

Bühlmann, H. (1970) Mathematical methods in risk theory. Spinger Verlag, New York.Google Scholar
de Finetti, B. (1940) Il problema dei pieni. Giorn. 1st. Ital. Attuari 11, 1–88.Google Scholar
Dickson, D.C.M. and Waters, H.R. (1993) Gamma processes and finite time survival probabilities. AST1N Bulletin 23, 259–272.Google Scholar
Dickson, D.C.M. and Waters, H.R. (1996) Reinsurance and ruin. Insurance: Mathematics & Economics 19, 61–80.Google Scholar
Grandell, J. (1977) A class of approximations of ruin probabilities. Scandinavian Actuarial Journal Supplement, 37–52.CrossRefGoogle Scholar
Ramlau-Hansen, H. (1983) Fire claims for single-family houses. Presented at the XVII ASTIN Colloquium, Lindau.Google Scholar
Ramlau-Hansen, H. (1986a) Statistical analysis of policy and claims data in non-life insurance: A solvency study. Part 1. Introduction to the study and analysis of glass claims. Working Paper No. 60, Laboratory of Actuarial Mathematics, University of Copenhagen.Google Scholar
Ramlau-Hansen, H. (1986b) Statistical analysis of policy and claims data in non-life insurance: A solvency study. Part 2. Analysis of fire claims. Working Paper No. 61, Laboratory of Actuarial Mathematics, University of Copenhagen.Google Scholar
Ramlau-Hansen, H. (1986c) Statistical analysis of policy and claims data in non-life insurance: A solvency study. Part 3. Analysis of windstorm claims. Working Paper No. 62, Laboratory of Actuarial Mathematics, University of Copenhagen.Google Scholar
Ramlau-Hansen, H. (1986d) Statistical analysis of policy and claims data in non-life insurance: A solvency study. Part 4. Analysis of windstorm claims. Working Paper No. 63, Laboratory of Actuarial Mathematics, University of Copenhagen.Google Scholar
Ramlau-Hansen, H. (1988a) A solvency study in non-life insurance. Part 1. Analyses of fire, windstorm and glass claims. Scandinavian Actuarial Journal, 3-34.Google Scholar
Ramlau-Hansen, H. (1988b) A solvency study in non-life insurance. Part 2. Solvency margin requirements. Scandinavian Actuarial Journal, 35–59.CrossRefGoogle Scholar