Journal of Applied Probability

An insensitivity property of Lundberg's estimate for delayed claims

Pierre Brémaud

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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.

Article information

J. Appl. Probab. Volume 37, Number 3 (2000), 914-917.

First available in Project Euclid: 27 February 2002

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 62P05: Applications to actuarial sciences and financial mathematics

Poisson shot noise ruin problem large deviations


Brémaud, Pierre. An insensitivity property of Lundberg's estimate for delayed claims. J. Appl. Probab. 37 (2000), no. 3, 914--917. doi:10.1239/jap/1014842846.

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