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An insensitivity property of Lundberg's estimate for delayed claims

Part of: Applications

Published online by Cambridge University Press:  14 July 2016

Pierre Brémaud
Pierre Brémaud*
Affiliation:
CNRS and École Polytechnique Fédérale de Lausanne
*
∗Postal address: Laboratoire des Signaux et Systèmes, CNRS-ESE, Plateau de Moulon, 91192 Gif-sur-Yvette, France. Email address: bremaud@lss.supelec.fr
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Abstract

This short note shows that the Lundberg exponential upper bound in the ruin problem of non-life insurance with compound Poisson claims is also valid for the Poisson shot noise delayed-claims model, and that the optimal exponent depends only on the distribution of the total claim per accident, not on the time it takes to honour the claim. This result holds under Cramer's condition.

Keywords

Poisson shot noiseruin problemlarge deviations

MSC classification

Primary: 62P05: Applications to actuarial sciences and financial mathematics
Type
Short Communications
Information
Journal of Applied Probability , Volume 37 , Issue 3 , September 2000 , pp. 914 - 917
Copyright
Copyright © Applied Probability Trust 2000 

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References

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