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On transform orders for largest claim amounts

Part of: Distribution theory - Probability Mathematical economics

Published online by Cambridge University Press:  22 November 2021

Yiying Zhang Open the ORCID record for Yiying Zhang [Opens in a new window]
Yiying Zhang*
Affiliation:
Southern University of Science and Technology
*
*Postal address: Department of Mathematics, Southern University of Science and Technology, Shenzhen 518055, Guangdong, China. Email: zhangyy3@sustech.edu.cn
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Abstract

This paper investigates the ordering properties of largest claim amounts in heterogeneous insurance portfolios in the sense of some transform orders, including the convex transform order and the star order. It is shown that the largest claim amount from a set of independent and heterogeneous exponential claims is more skewed than that from a set of independent and homogeneous exponential claims in the sense of the convex transform order. As a result, a lower bound for the coefficient of variation of the largest claim amount is established without any restrictions on the parameters of the distributions of claim severities. Furthermore, sufficient conditions are presented to compare the skewness of the largest claim amounts from two sets of independent multiple-outlier scaled claims according to the star order. Some comparison results are also developed for the multiple-outlier proportional hazard rates claims. Numerical examples are presented to illustrate these theoretical results.

Keywords

Largest claim amountskewnessstochastic ordersmajorizationscale modelPHR model

MSC classification

Primary: 91B16: Utility theory 91B30: Risk theory, insurance
Secondary: 60E15: Inequalities; stochastic orderings
Type
Original Article
Information
Journal of Applied Probability , Volume 58 , Issue 4 , December 2021 , pp. 1064 - 1085
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Copyright
© The Author(s), 2021. Published by Cambridge University Press on behalf of Applied Probability Trust

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