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Relative bound and asymptotic comparison of expectile with respect to expected shortfall

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  • Tadese, Mekonnen
  • Drapeau, Samuel

Abstract

Expectile bears some interesting properties in comparison to the industry wide expected shortfall in terms of assessment of tail risk. We study the relationship between expectile and expected shortfall using duality results and the link to optimized certainty equivalent. Lower and upper bounds of expectile are derived in terms of expected shortfall as well as a characterization of expectile in terms of expected shortfall. Further, we study the asymptotic behavior of expectile with respect to expected shortfall as the confidence level goes to 1 in terms of extreme value distributions. We use concentration inequalities to illustrate that the estimation of value at risk requires larger sample size than expected shortfall and expectile for heavy tail distributions when α is close to 1. Illustrating the formulation of expectile in terms of expected shortfall, we also provide explicit or semi-explicit expressions of expectile and some simulation results for some classical distributions.

Suggested Citation

  • Tadese, Mekonnen & Drapeau, Samuel, 2020. "Relative bound and asymptotic comparison of expectile with respect to expected shortfall," Insurance: Mathematics and Economics, Elsevier, vol. 93(C), pages 387-399.
    • Handle: RePEc:eee:insuma:v:93:y:2020:i:c:p:387-399
    DOI: 10.1016/j.insmatheco.2020.06.006
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    2. Zaevski, Tsvetelin S. & Nedeltchev, Dragomir C., 2023. "From BASEL III to BASEL IV and beyond: Expected shortfall and expectile risk measures," International Review of Financial Analysis, Elsevier, vol. 87(C).

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