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A Basic Asymptotic Test for Value-at-Risk Subadditivity

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  • Marius Hofert

    (Department of Statistics and Actuarial Science, School of Computing and Data Science, The University of Hong Kong, Hong Kong SAR, China)

Abstract

An asymptotic hypothesis test for value-at-risk subadditivity is introduced and studied. The test is derived based on an equivalent formulation of the value-at-risk subadditivity inequality in terms of the distribution of the underlying risks’ sum. Its size is considered mathematically, and its power and p -value are studied empirically for different dependence structures, strength of dependence, marginal distributions, sample sizes, number of risks and value-at-risk confidence levels.

Suggested Citation

  • Marius Hofert, 2024. "A Basic Asymptotic Test for Value-at-Risk Subadditivity," Risks, MDPI, vol. 12(12), pages 1-12, December.
    • Handle: RePEc:gam:jrisks:v:12:y:2024:i:12:p:199-:d:1540391
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    References listed on IDEAS

    as
    1. Paul Embrechts & Marius Hofert, 2013. "A note on generalized inverses," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 77(3), pages 423-432, June.
    2. Embrechts, Paul & Puccetti, Giovanni & Rüschendorf, Ludger, 2013. "Model uncertainty and VaR aggregation," Journal of Banking & Finance, Elsevier, vol. 37(8), pages 2750-2764.
    3. Hofert Marius & Memartoluie Amir & Saunders David & Wirjanto Tony, 2017. "Improved algorithms for computing worst Value-at-Risk," Statistics & Risk Modeling, De Gruyter, vol. 34(1-2), pages 13-31, June.
    4. Alexander J. McNeil & Rüdiger Frey & Paul Embrechts, 2015. "Quantitative Risk Management: Concepts, Techniques and Tools Revised edition," Economics Books, Princeton University Press, edition 2, number 10496.
    Full references (including those not matched with items on IDEAS)

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