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Dispersive orderings induced by differences of inter risk measures

Part of: Mathematical economics Distribution theory - Probability

Published online by Cambridge University Press:  12 October 2022

Keyi Zeng ,
Weiwei Zhuang  and
Taizhong Hu Open the ORCID record for Taizhong Hu [Opens in a new window]
Keyi Zeng*
Affiliation:
University of Science and Technology of China
Weiwei Zhuang*
Affiliation:
University of Science and Technology of China
Taizhong Hu*
Affiliation:
University of Science and Technology of China
*
*Postal address: Department of Statistics and Finance, IIF, School of Management, University of Science and Technology of China, Hefei, Anhui 230026, China.
*Postal address: Department of Statistics and Finance, IIF, School of Management, University of Science and Technology of China, Hefei, Anhui 230026, China.
*Postal address: Department of Statistics and Finance, IIF, School of Management, University of Science and Technology of China, Hefei, Anhui 230026, China.
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Abstract

In this short note we introduce two notions of dispersion-type variability orders, namely expected shortfall-dispersive (ES-dispersive) order and expectile-dispersive (ex-dispersive) order, which are defined by two classes of popular risk measures, the expected shortfall and the expectiles. These new orders can be used to compare the variability of two risk random variables. It is shown that either the ES-dispersive order or the ex-dispersive order is the same as the dilation order. This gives us some insight into parametric measures of variability induced by risk measures in the literature.

Keywords

Dispersive orderexpected shortfall-dispersive orderexpectile-dispersive orderconvex orderdilation order

MSC classification

Primary: 60E15: Inequalities; stochastic orderings
Secondary: 91B30: Risk theory, insurance
Type
Original Article
Information
Journal of Applied Probability , Volume 60 , Issue 1 , March 2023 , pp. 358 - 365
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Copyright
© The Author(s), 2022. Published by Cambridge University Press on behalf of Applied Probability Trust

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