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Asymptotic analysis of a dynamic systemic risk measure in a renewal risk model

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  • Li, Jinzhu

Abstract

In the context of insurance, we propose a dynamic systemic risk measure based on a multi-dimensional renewal risk model to describe the instant expected shortfall of an insurer at the moment when one of its business lines suffers crisis (i.e., deficit). The asymptotic behavior of the measure is studied in both the asymptotic independence and asymptotic dependence cases, and some asymptotic formulas with the uniformity in the whole time horizon are derived when the claim size distributions belong to the class of regular variation. The obtained results do not depend on specific setups of the renewal claim-number process, and they are also insensitive to specific dependence structures in the asymptotic independence case. These facts make our results concise in form and flexible in application. More interestingly, our results for the corresponding discounted version of the measure have nothing to do with the time variable. Hence, the discounted version of the measure can be regarded approximately as a static (i.e., time-invariant) risk measure of the dynamic system.

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  • Li, Jinzhu, 2022. "Asymptotic analysis of a dynamic systemic risk measure in a renewal risk model," Insurance: Mathematics and Economics, Elsevier, vol. 107(C), pages 38-56.
    • Handle: RePEc:eee:insuma:v:107:y:2022:i:c:p:38-56
    DOI: 10.1016/j.insmatheco.2022.07.012
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    Cited by:

    1. Bingzhen Geng & Yang Liu & Hongfu Wan, 2024. "Systemic Risk Asymptotics in a Renewal Model with Multiple Business Lines and Heterogeneous Claims," Papers 2410.00158, arXiv.org.

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    More about this item

    Keywords

    Dynamic systemic risk measure; Asymptotic behavior; Dependence; Regular variation;
    All these keywords.

    JEL classification:

    • C65 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Miscellaneous Mathematical Tools
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty

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