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Conditional Value at Risk and Partial Moments for the Metalog Distributions

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  • Valentyn Khokhlov

Abstract

The metalog distributions represent a convenient way to approach many practical applications. Their distinctive feature is simple closed-form expressions for quantile functions. This paper contributes to further development of the metalog distributions by deriving the closed-form expressions for the Conditional Value at Risk, a risk measure that is closely related to the tail conditional expectations. It also addressed the derivation of the first-order partial moments and shows that they are convex with respect to the vector of the metalog distribution parameters.

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  • Valentyn Khokhlov, 2021. "Conditional Value at Risk and Partial Moments for the Metalog Distributions," Papers 2102.10999, arXiv.org.
    • Handle: RePEc:arx:papers:2102.10999
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    References listed on IDEAS

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    1. Thomas W. Keelin, 2016. "The Metalog Distributions," Decision Analysis, INFORMS, vol. 13(4), pages 243-277, December.
    2. Philippe Artzner & Freddy Delbaen & Jean‐Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, vol. 9(3), pages 203-228, July.
    3. Matthew Norton & Valentyn Khokhlov & Stan Uryasev, 2018. "Calculating CVaR and bPOE for Common Probability Distributions With Application to Portfolio Optimization and Density Estimation," Papers 1811.11301, arXiv.org, revised Feb 2019.
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