Abstract
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.
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Tang, Q. An asymptotic relationship for ruin probabilities under heavy-tailed claims. Sci. China Ser. A-Math. 45, 632–639 (2002). https://doi.org/10.1360/02ys9068
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DOI: https://doi.org/10.1360/02ys9068