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

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 ψ_δ (u) ∼ κ_δ (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.

Key words:

• Abel-Tauber theorems
• heavy tails
• interest rate model
• modified Laplace transforms
• regular variation
• ruin probability