Hostname: page-component-586b7cd67f-tf8b9 Total loading time: 0 Render date: 2024-11-23T12:41:28.137Z Has data issue: false hasContentIssue false
  • English
  • Français

Estimators and Bootstrap Confidence Intervals for Ruin Probabilities

Published online by Cambridge University Press:  29 August 2014

Christian Hipp
Christian Hipp*
Affiliation:
University of Hamburg, FRG
*
Universität Hamburg, Institut für mathematische Stochastik, Bundesstrasse 55, D-2000 Hamburg 13.
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.

For the infinite time ruin probability in the classical risk process, efficient estimators are proposed in cases in which the claim amount distribution is unknown. Confidence intervals are computed which are based on normal approximations or on the bootstrap method. The procedures are checked in a Monte-Carlo study.

Keywords

Infinite time ruin probabilitiesnonparametric estimatorsconfidence intervalsbootstrap method
Type
Articles
Information
ASTIN Bulletin: The Journal of the IAA , Volume 19 , Issue 1 , April 1989 , pp. 57 - 70
Copyright
Copyright © International Actuarial Association 1989

References

Bühlmann, H. (1980). Mathematical methods in risk theory. Springer, New York.Google Scholar
Engeländer, S. (1987). Konfidenzintervalle für empirische Ruinwahrscheinlickeiten: asymptotisches Verhalten und Monte-Carlo-Simulation. Diploma Thesis, University of Cologne.Google Scholar
Feller, W. (1970) An Introduction to Probability Theory and Its Applications, 2, Wiley, New York.Google Scholar
Frees, E. W. (1986). Nonparametric estimation of the probability of ruin. ASTIN Bulletin 16, 81–90.CrossRefGoogle Scholar
Grandell, J. (1979). Empirical bounds for ruin probabilities. Stoch Process and Their Applications 8, 243–255.CrossRefGoogle Scholar
Hipp, C. (1988). Efficient estimators for ruin probabilities. Proc. 4th Prague Symp. Asympt. Statist.Google Scholar
Taylor, G. C. (1985). A heuristic review of some ruin theory results. ASTIN Bulletin 15, 73–88.CrossRefGoogle Scholar