Science in China Series A: Mathematics

, Volume 45, Issue 5, pp 632–639 | Cite as

An asymptotic relationship for ruin probabilities under heavy-tailed claims

  • Qihe Tang


The famous Embrechts-Goldie-Veraverbeke formula shows that, in the classical Cramér-Lundberg risk model, the ruin probabilities satisfy \(R(x, \infty ) \sim \rho ^{ - 1} \bar F_e (x)\) if the claim sizes are heavy-tailed, where Fe denotes the equilibrium distribution of the common d.f. F of the i.i.d. claims, ? is the safety loading coefficient of the model and the limit process is for x → ∞. In this paper we obtain a related local asymptotic relationship for the ruin probabilities. In doing this we establish two lemmas regarding the n-fold convolution of subexponential equilibrium distributions, which are of significance on their own right.


Cramér-Lundberg model geometric sums heavy-tailed distribution ladder height ruin probabilities 


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Copyright information

© Science in China Press 2002

Authors and Affiliations

  1. 1.Department of Statistics and FinanceUniversity of Science and Technology of ChinaHefeiChina

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