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Estimations and asymptotic behaviors of coherent entropic risk measure for sums of random variables

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  • Yan, Jun

Abstract

In this article, we provide an estimation and several asymptotic behaviors for the coherent entropic risk measure of compound Poisson process. We also establish an estimation for the coherent entropic risk measure of sum of i.i.d. random variables in virtue of Log-Sobolev inequality. As an application, we provide two deviation estimations of the tail probability for compound Poisson process. Finally, several simulation results are given to support our results.

Suggested Citation

  • Yan, Jun, 2014. "Estimations and asymptotic behaviors of coherent entropic risk measure for sums of random variables," Statistics & Probability Letters, Elsevier, vol. 91(C), pages 171-180.
    • Handle: RePEc:eee:stapro:v:91:y:2014:i:c:p:171-180
    DOI: 10.1016/j.spl.2014.04.019
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    1. Massimo Pierro & Jack Mosevich, 2011. "Effects of skewness and kurtosis on portfolio rankings," Quantitative Finance, Taylor & Francis Journals, vol. 11(10), pages 1449-1453.
    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. Deprez, Olivier & Gerber, Hans U., 1985. "On convex principles of premium calculation," Insurance: Mathematics and Economics, Elsevier, vol. 4(3), pages 179-189, July.
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