Ruin probabilities in the presence of heavy-tails and interest rates

Claudia Klüppelberg and Ulrich Stadtmüller

Scandinavian Actuarial Journal, 1998, vol. 1998, issue 1, 49-58

Abstract: We study the infinite time ruin probability for the classical Cramér-Lundberg model, where the company also receives interest on its reserve. We consider the large claims case, where the claim size distribution F has a regularly varying tail. Hence our results apply for instance to Pareto, loggamma, certain Benktander and stable claim size distributions. We prove that for a positive force of interest δ the ruin probability ψδ(u) ∼ κδ(1 - F(u)) as the initial risk reserve u→∞. This is quantitatively different from the non-interest model, where ψ(u) ∼ κ (1 – F(y)) dy.

Date: 1998
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DOI: 10.1080/03461238.1998.10413991

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