Abstract
A distortion risk measure used in finance and insurance is defined as the expected value of potential loss under a scenario probability measure. In this paper, the tail distortion risk measure is introduced to assess tail risks of excess losses modeled by the right tails of loss distributions. The asymptotic linear relation between tail distortion and value-at-risk is derived for heavy-tailed losses with the linear proportionality constant depending only on the distortion function and the tail index. Various examples involving tail distortions for location-invariant, scale-invariant, and shape-invariant loss distribution families are also presented to illustrate the results.
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