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 fit generalized Pareto distributions. The proposed
strategy is compared to standard parametric modeling based on gamma, lognormal, and log …

values of the threshold. The results of the estimations are summarized in Table 1; this table
should be compared with Table 3 on p. 25 of Cébrian et al. Within the new model, we can
test the adequacy of the GPD by a likelihood ratio test of the null-hypothesis 1. The GPD is
strongly rejected for all small threshold values (see Figure 1). Only for threshold values
larger than $100,000, the GPD model is not rejected, which is in line with the findings of
Cébrian et al. A similar conclusion follows from the point estimates ˆ and their standard …