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ON HETEROGENEITY IN THE INDIVIDUAL MODEL WITH BOTH DEPENDENT CLAIM OCCURRENCES AND SEVERITIES

Published online by Cambridge University Press:  15 February 2018

Yiying Zhang ,
Xiaohu Li  and
Ka Chun Cheung
Yiying Zhang*
Affiliation:
Department of Statistics and Actuarial Science, The University of Hong Kong, Pokfulam Road, Hong Kong
Xiaohu Li
Affiliation:
Department of Mathematical Sciences, Stevens Institute of Technology, Hoboken, NJ 07030, USA E-mail: mathxli@hotmail.com
Ka Chun Cheung
Affiliation:
Department of Statistics and Actuarial Science, The University of Hong Kong, Pokfulam Road, Hong Kong E-mail: kccg@hku.hk
*
E-mail: zhyy@hku.hk, zhangyiying@outlook.com
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Abstract

It is a common belief for actuaries that the heterogeneity of claim severities in a given insurance portfolio tends to increase its dangerousness, which results in requiring more capital for covering claims. This paper aims to investigate the effects of orderings and heterogeneity among scale parameters on the aggregate claim amount when both claim occurrence probabilities and claim severities are dependent. Under the assumption that the claim occurrence probabilities are left tail weakly stochastic arrangement increasing, the actuaries' belief is examined from two directions, i.e., claim severities are comonotonic or right tail weakly stochastic arrangement increasing. Numerical examples are provided to validate these theoretical findings. An application in assets allocation is addressed as well.

Keywords

MajorizationcomonotonicityRWSAILWSAIstop-loss order
Type
Research Article
Information
ASTIN Bulletin: The Journal of the IAA , Volume 48 , Issue 2 , May 2018 , pp. 817 - 839
Copyright
Copyright © Astin Bulletin 2018 

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