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Ruin probabilities in the presence of heavy-tails and interest rates. (English) Zbl 1022.60083
Summary: 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 \(\delta\) the ruin probability \(\psi_\delta(u)\sim \kappa_\delta(1- F(u))\) as the initial risk reserve \(u\to\infty\). This is quantitatively different from the non-interest model, where \(\psi(u)\sim\kappa \int^\infty_u (1- F(y)) dy\).

MSC:
60K10 Applications of renewal theory (reliability, demand theory, etc.)
91B30 Risk theory, insurance (MSC2010)
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