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Probability equivalent level of Value at Risk and higher-order Expected Shortfalls

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  • Matyas Barczy
  • Fanni K. Ned'enyi
  • L'aszl'o SutH{o}

Abstract

We investigate the probability equivalent level of Value at Risk and $n^{\mathrm{th}}$-order Expected Shortfall (called PELVE_n), which can be considered as a variant of the notion of the probability equivalent level of Value at Risk and Expected Shortfall (called PELVE) due to Li and Wang (2022). We study the finiteness, uniqueness and several properties of PELVE_n, we calculate PELVE_n of some notable distributions, PELVE_2 of a random variable having generalized Pareto excess distribution, and we describe the asymptotic behaviour of PELVE_2 of regularly varying distributions as the level tends to $0$. Some properties of $n^{\mathrm{th}}$-order Expected Shortfall are also investigated. Among others, it turns out that the Gini Shortfall at some level $p\in[0,1)$ corresponding to a (loading) parameter $\lambda\geq 0$ is the linear combination of the Expected Shortfall at level $p$ and the $2^{\mathrm{nd}}$-order Expected Shortfall at level $p$ with coefficients $1-2\lambda$ and $2\lambda$, respectively.

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  • Matyas Barczy & Fanni K. Ned'enyi & L'aszl'o SutH{o}, 2022. "Probability equivalent level of Value at Risk and higher-order Expected Shortfalls," Papers 2202.09770, arXiv.org, revised Nov 2022.
  • Handle: RePEc:arx:papers:2202.09770
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    References listed on IDEAS

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    Cited by:

    1. Hirbod Assa & Liyuan Lin & Ruodu Wang, 2022. "Calibrating distribution models from PELVE," Papers 2204.08882, arXiv.org, revised Jun 2023.

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