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Deviations of convex and coherent entropic risk measures

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  • Yan, Jun

Abstract

In this article, we establish several deviations for convex and coherent entropic risk measures. Firstly, we provide several deviations for the two risk measures with respect to relative entropy. Secondly, we provide several deviations for the two risk measures with respect to parameters. Thirdly, we study the continuity properties of the two risk measures with respect to the random variables under several norms. Finally, we establish an application of our main results.

Suggested Citation

  • Yan, Jun, 2015. "Deviations of convex and coherent entropic risk measures," Statistics & Probability Letters, Elsevier, vol. 100(C), pages 56-66.
    • Handle: RePEc:eee:stapro:v:100:y:2015:i:c:p:56-66
    DOI: 10.1016/j.spl.2015.01.035
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    References listed on IDEAS

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    1. Paul Embrechts & Giovanni Puccetti & Ludger Rüschendorf & Ruodu Wang & Antonela Beleraj, 2014. "An Academic Response to Basel 3.5," Risks, MDPI, vol. 2(1), pages 1-24, February.
    2. A. Ahmadi-Javid, 2012. "Entropic Value-at-Risk: A New Coherent Risk Measure," Journal of Optimization Theory and Applications, Springer, vol. 155(3), pages 1105-1123, December.
    3. Aharon Ben‐Tal & Marc Teboulle, 2007. "An Old‐New Concept Of Convex Risk Measures: The Optimized Certainty Equivalent," Mathematical Finance, Wiley Blackwell, vol. 17(3), pages 449-476, July.
    4. Paul Embrechts & Bin Wang & Ruodu Wang, 2015. "Aggregation-robustness and model uncertainty of regulatory risk measures," Finance and Stochastics, Springer, vol. 19(4), pages 763-790, October.
    5. Krätschmer, Volker & Schied, Alexander & Zähle, Henryk, 2012. "Qualitative and infinitesimal robustness of tail-dependent statistical functionals," Journal of Multivariate Analysis, Elsevier, vol. 103(1), pages 35-47, January.
    6. Hans Föllmer & Stefan Weber, 2015. "The Axiomatic Approach to Risk Measures for Capital Determination," Annual Review of Financial Economics, Annual Reviews, vol. 7(1), pages 301-337, December.
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    Cited by:

    1. Brandtner, Mario & Kürsten, Wolfgang & Rischau, Robert, 2018. "Entropic risk measures and their comparative statics in portfolio selection: Coherence vs. convexity," European Journal of Operational Research, Elsevier, vol. 264(2), pages 707-716.

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