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Nonparametric estimation of risk measures of collective risks

Authors
  • Lauer, Alexandra
  • Zähle, Henryk
Type
Preprint
Publication Date
Sep 16, 2015
Submission Date
Apr 10, 2015
Identifiers
arXiv ID: 1504.02693
Source
arXiv
License
Yellow
External links

Abstract

We consider two nonparametric estimators for the risk measure of the sum of $n$ i.i.d. individual insurance risks where the number of historical single claims that are used for the statistical estimation is of order $n$. This framework matches the situation that nonlife insurance companies are faced with within in the scope of premium calculation. Indeed, the risk measure of the aggregate risk divided by $n$ can be seen as a suitable premium for each of the individual risks. For both estimators divided by $n$ we derive a sort of Marcinkiewicz--Zygmund strong law as well as a weak limit theorem. The behavior of the estimators for small to moderate $n$ is studied by means of Monte-Carlo simulations.

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