6533b821fe1ef96bd127b939

RESEARCH PRODUCT

Ruin probabilities in the presence of heavy tails and interest rates

Claudia KlüppelbergUlrich Stadtmüller

subject

Statistics and ProbabilityEconomics and Econometricsmedia_common.quotation_subjectPareto principleInterest rateActuarial notationddc:Distribution (mathematics)Short-rate modelStatistical physicsStatistics Probability and UncertaintyMathematical economicsmedia_commonMathematics

description

Abstract We study the infinite time ruin probability for the classical Cramer-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.

10.1080/03461238.1998.10413991https://mediatum.ub.tum.de/1120624