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Derivatives of Risk Measures

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  • Battulga Gankhuu

Abstract

This paper provides the first and second order derivatives of any risk measures, including VaR and ES for continuous and discrete portfolio loss random variable variables. Also, we give asymptotic results of the first and second order conditional moments for heavy-tailed portfolio loss random variable.

Suggested Citation

  • Battulga Gankhuu, 2024. "Derivatives of Risk Measures," Papers 2404.09646, arXiv.org, revised Aug 2024.
    • Handle: RePEc:arx:papers:2404.09646
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    References listed on IDEAS

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    1. Acerbi, Carlo & Tasche, Dirk, 2002. "On the coherence of expected shortfall," Journal of Banking & Finance, Elsevier, vol. 26(7), pages 1487-1503, July.
    2. 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.
    3. Gourieroux, C. & Laurent, J. P. & Scaillet, O., 2000. "Sensitivity analysis of Values at Risk," Journal of Empirical Finance, Elsevier, vol. 7(3-4), pages 225-245, November.
    4. Venter, Gary G. & Major, John A. & Kreps, Rodney E., 2006. "Marginal Decomposition of Risk Measures," ASTIN Bulletin, Cambridge University Press, vol. 36(2), pages 375-413, November.
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