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Stochastic orders and distortion risk contribution ratio measures

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  • Zhang, Yiying

Abstract

Relative spillover effects play a crucial role in the analysis and comparison of systemic risks. This paper introduces a novel approach, referred to as distortion risk contribution ratio measures, for quantifying such effects. Various types of contribution ratio measures are defined based on the newly proposed conditional distortion risk measures by Dhaene et al. (2022), and useful integral-based representations are provided as well. An interesting equivalent characterization result for the convex transform order is also presented, which is not only relevant to proving our main results but also has independent value in other research areas. We then establish comparison results between the distortion risk contribution ratio measures of two different bivariate random vectors with either the same or different copulas. Sufficient conditions are established in terms of stochastic orders, copula functions, distortion functions, and stress levels. Furthermore, we investigate the ordering behaviors of these measures in relation to the interaction between paired risks. Numerical examples are presented to illustrate the conditions and main findings.

Suggested Citation

  • Zhang, Yiying, 2024. "Stochastic orders and distortion risk contribution ratio measures," Insurance: Mathematics and Economics, Elsevier, vol. 118(C), pages 104-122.
    • Handle: RePEc:eee:insuma:v:118:y:2024:i:c:p:104-122
    DOI: 10.1016/j.insmatheco.2024.06.007
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    More about this item

    Keywords

    Risk contribution; Ratio measure; Systemic risk; Convex transform order; Star order; Copula;
    All these keywords.

    JEL classification:

    • G21 - Financial Economics - - Financial Institutions and Services - - - Banks; Other Depository Institutions; Micro Finance Institutions; Mortgages
    • G22 - Financial Economics - - Financial Institutions and Services - - - Insurance; Insurance Companies; Actuarial Studies
    • G31 - Financial Economics - - Corporate Finance and Governance - - - Capital Budgeting; Fixed Investment and Inventory Studies

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