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

Claudia Klüppelberg · Ulrich Stadtmüller

113 citations0/0 files storedScandinavian Actuarial Journal

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Probability and Risk Models Insurance and Financial Risk Management Probability and Statistical Research

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.

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References

1997Modelling Extremal Events 1994Modelling of extremal events in insurance and finance 1987Applied Probability and Queues 1991Aspects of Risk Theory 1982Estimates for the probability of ruin with special emphasis on the possibility of large claims 1988Subexponential distributions and integrated tails 1980On closure and factorization properties of subexponential and related distributions 1995Ruin estimates under interest force

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