6533b821fe1ef96bd127b939
RESEARCH PRODUCT
Ruin probabilities in the presence of heavy tails and interest rates
Claudia KlüppelbergUlrich Stadtmüllersubject
Statistics and ProbabilityEconomics and Econometricsmedia_common.quotation_subjectPareto principleInterest rateActuarial notationddc:Distribution (mathematics)Short-rate modelStatistical physicsStatistics Probability and UncertaintyMathematical economicsmedia_commonMathematicsdescription
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.
year | journal | country | edition | language |
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1997-11-30 |