Estimating ruin probabilities in the Cramér-Lundberg model with heavy-tailed claims

Ruin probability is the key indicator of an unbalanced cash flow and/or insufficient operating capital for an insurance company. This thesis studies how to use Pollaczeck-Khinchine formula to estimate the ruin probability by means of simulations when the only assumption apart from the Cramér-Lundberg insurance risk model is the fact that claims have heavy-tailed distribution. Approximation of the integrated tail distribution for claim size data is the key problem in the thesis, where generalized Pareto distribution as a basic extreme-value tool plays a very important role. Moreover, empirical distribution function of the claims is combined with the generalized Pareto distribution when approximating claim size distribution. Also, the properties of the integrated tail distribution are derived and its simulation considered. Proposed methodology is applied to a real insurance claims data set.

Author

• Kaasik, Ants

Identifier

hdl:10062/14195

OAI identifier oai:identifier

oai:dspace.ut.ee:10062/14195