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On tail-risk measures for non integrable heavy-tailed random variables

Abstract : The assessment of risk is a crucial question in various fields of application. An important family of risk measures is provided by the class of distortion risk measures. However, the use of these risk measures is limited by an integrability condition on the quantile function. When heavy-tailed distributions are considered, this condition is violated when the tail index becomes large. In this paper, we first propose a new family of risk measures obtained by minimizing a set of distortion risk measures over a class of probability measures. When a heavy-tailed distribution is considered, we pick in this class a new risk measure whose main feature is to be defined whatever the value of the tail index. The asymptotic behavior of its tail version is investigated and a consistent estimator is proposed. The finite sample performance is discussed on a fire claims dataset.
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https://hal.archives-ouvertes.fr/hal-03369353
Contributor : Laurent Gardes Connect in order to contact the contributor
Submitted on : Thursday, October 7, 2021 - 12:22:44 PM
Last modification on : Tuesday, October 12, 2021 - 3:39:13 AM

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  • HAL Id : hal-03369353, version 1

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Laurent Gardes. On tail-risk measures for non integrable heavy-tailed random variables. 2021. ⟨hal-03369353⟩

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