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Generalized Pareto fit to the society of actuaries’ large claims database. (English) Zbl 1084.62108

Summary: 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-gamma distributions. Extreme value theory outperforms classical parametric fits and allows the actuary to easily estimate high quantiles and the probable maximum loss from the data.

MSC:

62P05 Applications of statistics to actuarial sciences and financial mathematics
62G32 Statistics of extreme values; tail inference
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