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MODELLING INSURANCE LOSSES USING CONTAMINATED GENERALISED BETA TYPE-II DISTRIBUTION

Published online by Cambridge University Press:  09 March 2018

J.S.K. Chan ,
S.T.B. Choy ,
U.E. Makov  and
Z. Landsman
J.S.K. Chan*
Affiliation:
School of Mathematics and Statistics, The University of Sydney, NSW 2006, Australia Actuarial Research Center, University of Haifa, Haifa, Israel
S.T.B. Choy
Affiliation:
Disciplines of Business Analytics, The University of Sydney, NSW 2006, Australia Actuarial Research Center, University of Haifa, Haifa, Israel E-mail: boris.choy@sydney.edu.au
U.E. Makov
Affiliation:
Department of Statistics, Actuarial Research Center, University of Haifa, Haifa, 31905, Israel E-mail: makov@stat.haifa.ac.il
Z. Landsman
Affiliation:
Department of Statistics, Actuarial Research Center, University of Haifa, Haifa, 31905, Israel E-mail: landsman@stat.haifa.ac.il
*
E-mail: jchan@maths.usyd.edu.au
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Abstract

The four-parameter distribution family, the generalised beta type-II (GB2), also known as the transformed beta distribution, has been proposed for modelling insurance losses. As special cases, this family nests many distributions with light and heavy tails, including the lognormal, gamma, Weibull, Burr and generalised gamma distributions. This paper extends the GB2 family to the contaminated GB2 family, which offers many flexible features, including bimodality and a wide range of skewness and kurtosis. Properties of the contaminated distribution are derived and evaluated in a simulation study and the suitability of the contaminated GB2 distribution for actuarial purposes is demonstrated through two real loss data sets. Analysis of tail quantiles for the data suggests large differences in extreme quantile estimates for different loss distribution assumptions, showing that the selection of appropriate distributions has a significant impact for insurance companies.

Keywords

Loss distributiongeneralised beta type-II distributioncontaminated mixture distributionBayesian MCMCValue-at-Risktail conditional expectationEM algorithm
Type
Research Article
Information
ASTIN Bulletin: The Journal of the IAA , Volume 48 , Issue 2 , May 2018 , pp. 871 - 904
Copyright
Copyright © Astin Bulletin 2018 

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