zInstitut des Sciences Actuarielles

This paper discusses a statistical modeling strategy based on extreme value theory to describe the behavior of an insurance portfolio, with particular emphasis on large claims. The strategy is illustrated using the 1991-92 group medical claims database maintained by the Society of Actuaries. Using extreme value theory, the modeling strategy focuses on the \excesses over threshold " approach to t Generalized Pareto distributions. The proposed strategy is compared to standard parametric modeling based on Gamma, LogNormal and LogGamma distributions. Extreme value theory outperforms classical parametric ts and allows the actuary to easily estimate high quantiles and the probable maximum loss from the data. Key words and phrases: large claims, extreme value theory, generalized Pareto distri-bution, generalized extreme value distribution, excesses over threshold method, probable maximum loss. G220 Insurance C190 Econometric and statistical methods