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Estimation of Distortion Risk Measures

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  • Hideatsu Tsukahara

Abstract

For the class of distortion risk measures, a natural estimator has the form of L-statistics. In this article, we investigate the large sample properties of general L-statistics based on weakly dependent data and apply them to our estimator. Under certain regularity conditions, which are somewhat weaker than the ones found in the literature, we prove that the estimator is strongly consistent and asymptotically normal. Furthermore, we give a consistent estimator for its asymptotic variance using spectral density estimators of a related stationary sequence. The behavior of the estimator is examined using simulation in two examples: inverse-gamma autoregressive stochastic volatility model and GARCH(1,1). Copyright The Author, 2013. Published by Oxford University Press. All rights reserved. For Permissions, please email: journals.permissions@oup.com, Oxford University Press.

Suggested Citation

  • Hideatsu Tsukahara, 2013. "Estimation of Distortion Risk Measures," Journal of Financial Econometrics, Oxford University Press, vol. 12(1), pages 213-235, December.
    • Handle: RePEc:oup:jfinec:v:12:y:2013:i:1:p:213-235
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    File URL: http://hdl.handle.net/10.1093/jjfinec/nbt005
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    Citations

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    Cited by:

    1. Volker Krätschmer & Alexander Schied & Henryk Zähle, 2014. "Comparative and qualitative robustness for law-invariant risk measures," Finance and Stochastics, Springer, vol. 18(2), pages 271-295, April.
    2. Suparna Biswas & Rituparna Sen, 2019. "Kernel Based Estimation of Spectral Risk Measures," Papers 1903.03304, arXiv.org, revised Dec 2023.
    3. Debora Daniela Escobar & Georg Ch. Pflug, 2020. "The distortion principle for insurance pricing: properties, identification and robustness," Annals of Operations Research, Springer, vol. 292(2), pages 771-794, September.
    4. Daniela Escobar & Georg Pflug, 2018. "The distortion principle for insurance pricing: properties, identification and robustness," Papers 1809.06592, arXiv.org.
    5. Darinka Dentcheva & Spiridon Penev & Andrzej Ruszczyński, 2017. "Statistical estimation of composite risk functionals and risk optimization problems," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 69(4), pages 737-760, August.
    6. Eric Beutner & Henryk Zähle, 2018. "Bootstrapping Average Value at Risk of Single and Collective Risks," Risks, MDPI, vol. 6(3), pages 1-30, September.
    7. Sun, Xianming & Gan, Siqing & Vanmaele, Michèle, 2015. "Analytical approximation for distorted expectations," Statistics & Probability Letters, Elsevier, vol. 107(C), pages 246-252.

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