Hostname: page-component-586b7cd67f-vdxz6 Total loading time: 0 Render date: 2024-11-22T05:07:01.676Z Has data issue: false hasContentIssue false
  • English
  • Français

On the De Vylder and Goovaerts Conjecture About Ruin for Equalized Claims

Part of: Special processes Stochastic processes

Published online by Cambridge University Press:  30 January 2018

C. Y. Robert
C. Y. Robert*
Affiliation:
Université de Lyon and Université Claude Bernard Lyon 1
*
∗ Postal address: Institut de Science Financière et d'Assurances, Université Claude Bernard Lyon 1, 50 avenue Tony Garnier, 69366 Lyon Cedex 07, France. Email address: [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.

In ruin theory, the conjecture given in De Vylder and Goovaerts (2000) is an open problem about the comparison of the finite time ruin probability in a homogeneous risk model and the corresponding ruin probability evaluated in the associated model with equalized claim amounts. In this paper we consider a weaker version of the conjecture and show that the integrals of the ruin probabilities with respect to the initial risk reserve are uniformly comparable.

Keywords

De Vylder and Goovaerts' conjecturehomogeneous risk modelfinite time ruin probabilitystochastic dominance

MSC classification

Primary: 60G50: Sums of independent random variables; random walks 60G09: Exchangeability
Secondary: 60K30: Applications (congestion, allocation, storage, traffic, etc.)
Type
Research Article
Information
Journal of Applied Probability , Volume 51 , Issue 3 , September 2014 , pp. 874 - 879
Copyright
© Applied Probability Trust 

References

De Vylder, F. and Goovaerts, M. (2000). Homogeneous risk models with equalized claim amounts. Insurance Math. Econom. 26, 223–238.Google Scholar
Denuit, M., Dhaene, J., Goovaerts, M. and Kaas, R. (2005). Actuarial Theory for Dependent Risks: Measures, Orders and Models. John Wiley, New York.Google Scholar
Lefèvre, C. and Picard, P. (2011). A new look at the homogeneous risk model. Insurance Math. Econom. 49, 512–519.Google Scholar
Marshall, A. W., Olkin, I. and Arnold, B. C. (2011). Inequalities: Theory of Majorization and Its Applications. Springer, New York.CrossRefGoogle Scholar
Reiss, R.-D. (1989). Approximate Distributions of Order Statistics. With Applications to Nonparamentric Statistics. Springer, New York.CrossRefGoogle Scholar
Spitzer, F. (1956). A combinatorial lemma and its application to probability theory. Trans. Amer. Math. Soc. 82, 323–339.Google Scholar