Extreme value theory for detecting heavy tails of large claims
Extreme value theory for detecting heavy tails of large claims

Summary/Abstract: One of the most prominent facets, that arises in risk management in an insurance company, is a difficulty in detecting large claims’ distribution properly. Therefore, a quite large variety of stochastic methods and models have been proposed to solve the mentioned difficulty. The main goal of the presented study is to discuss and to compare two alternative approaches to theoretical distribution estimation. The first approach consists in collective es-timation of all parameters of theoretical distribution, while the second approach is based on two-step procedure, in which previous estimation of tail-heaviness parameter is followed by conditional estimation of the rest of parameters. The theoretic discussion is illustrated by simulation research and empirical data analysis, as well. As a result, one may state that the introduced two-step approach enables more flexible, and adequate detection of tail asymp-totics without negative impact on a quality of the remaining parameters’ estimates.

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