Nonparametric estimation of risk measures of collective risks

Lauer Alexandra () and Zähle Henryk ()
Additional contact information
Lauer Alexandra: Department of Mathematics, Saarland University, Postfach 151150, 66041 Saarbrücken, Germany
Zähle Henryk: Department of Mathematics, Saarland University, Postfach 151150, 66041 Saarbrücken, Germany

Statistics & Risk Modeling, 2016, vol. 32, issue 2, 89-102

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 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.

Keywords: Aggregate risk; total claim distribution; convolution; law-invariant risk measure; nonuniform Berry–Esséen inequality; Marcinkiewicz–Zygmund strong law; weak limit theorem; Panjer recursion (search for similar items in EconPapers)
Date: 2016
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://doi.org/10.1515/strm-2015-0014 (text/html)
For access to full text, subscription to the journal or payment for the individual article is required.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:bpj:strimo:v:32:y:2016:i:2:p:89-102:n:3

Ordering information: This journal article can be ordered from
https://www.degruyter.com/journal/key/strm/html

DOI: 10.1515/strm-2015-0014

Access Statistics for this article

Statistics & Risk Modeling is currently edited by Robert Stelzer

More articles in Statistics & Risk Modeling from De Gruyter
Bibliographic data for series maintained by Peter Golla ().