Modelling losses and locating the tail with the Pareto Positive Stable distribution
Montserrat Guillen,
Faustino Prieto and
José María Sarabia ()
Insurance: Mathematics and Economics, 2011, vol. 49, issue 3, 454-461
Abstract:
This paper focuses on modelling the severity distribution. We directly model the small, moderate and large losses with the Pareto Positive Stable (PPS) distribution and thus it is not necessary to fix a threshold for the tail behaviour. Estimation with the method of moments is straightforward. Properties, graphical tests and expressions for value-at risk and tail value-at-risk are presented. Furthermore, we show that the PPS distribution can be used to construct a statistical test for the Pareto distribution and to determine the threshold for the Pareto shape if required. An application to loss data is presented. We conclude that the PPS distribution can perform better than commonly used distributions when modelling a single loss distribution for moderate and large losses. This approach avoids the pitfalls of cut-off selection and it is very simple to implement for quantitative risk analysis.
Keywords: Pareto distribution; Positive stable law; Loss model; Severity distribution (search for similar items in EconPapers)
Date: 2011
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (22)
Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0167668711000813
Full text for ScienceDirect subscribers only
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:eee:insuma:v:49:y:2011:i:3:p:454-461
DOI: 10.1016/j.insmatheco.2011.07.004
Access Statistics for this article
Insurance: Mathematics and Economics is currently edited by R. Kaas, Hansjoerg Albrecher, M. J. Goovaerts and E. S. W. Shiu
More articles in Insurance: Mathematics and Economics from Elsevier
Bibliographic data for series maintained by Catherine Liu ().