Equivalent distortion risk measures on moment spaces

Dries Cornilly; Steven Vanduffel

doi:10.1016/j.spl.2018.11.021

Equivalent distortion risk measures on moment spaces

Research output: Contribution to journal › Article › peer-review

Abstract

We show that maximizing distortion risk measures over the set of distributions with given mean is equivalent to maximizing their concave counterpart. In the case of Value-at-Risk and Tail Value-at-Risk the equivalence also holds when adding information on higher moments.

Original language	English
Pages (from-to)	187-192
Number of pages	6
Journal	Statistics and Probability Letters
Volume	146
DOIs	https://doi.org/10.1016/j.spl.2018.11.021
Publication status	Published - 1 Mar 2019

Keywords

Coherent risk measure
Distortion function
Expected shortfall (ES)
Model uncertainty
Value-at-Risk (VaR)

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10.1016/j.spl.2018.11.021

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title = "Equivalent distortion risk measures on moment spaces",

abstract = "We show that maximizing distortion risk measures over the set of distributions with given mean is equivalent to maximizing their concave counterpart. In the case of Value-at-Risk and Tail Value-at-Risk the equivalence also holds when adding information on higher moments.",

keywords = "Coherent risk measure, Distortion function, Expected shortfall (ES), Model uncertainty, Value-at-Risk (VaR)",

author = "Dries Cornilly and Steven Vanduffel",

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doi = "10.1016/j.spl.2018.11.021",

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AU - Vanduffel, Steven

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AB - We show that maximizing distortion risk measures over the set of distributions with given mean is equivalent to maximizing their concave counterpart. In the case of Value-at-Risk and Tail Value-at-Risk the equivalence also holds when adding information on higher moments.

KW - Coherent risk measure

KW - Distortion function

KW - Expected shortfall (ES)

KW - Model uncertainty

KW - Value-at-Risk (VaR)

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DO - 10.1016/j.spl.2018.11.021

M3 - Article

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JO - Statistics & Probability Letters

JF - Statistics & Probability Letters

SN - 0167-7152

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Equivalent distortion risk measures on moment spaces

Abstract

Keywords

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