Monotone tail functions: Definitions, properties, and application to risk-reducing strategies

Hanbali, Hamza; Linders, Daniël

doi:10.1016/j.cam.2022.114484

Cited by 2 publications

(2 citation statements)

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“…In such situations, the existing decompositions are not valid. Hanbali and Linders (2021) provide decompositions for the VaR of comonotonic differences under more general assumptions using the concept of tail monotone functions, where the decomposition holds for certain values of the quantile level. Their results can readily be applied to decompose the TVaR as well, but only at confidence levels beyond some thresholds.…”

Section: Introductionmentioning

confidence: 99%

“…The situation where g is not monotone is problematic. Hanbali and Linders (2021) address the problem and show that the equality F −1 g(X) (p) = g F −1 X (p) holds for specific values of p if the function g has a monotone tail. The present paper adds to their insights by showing that if g is not monotone, then that equality does not necessarily hold.…”

Section: Introductionmentioning

confidence: 99%

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Value-at-Risk, Tail Value-at-Risk and upper tail transform of the sum of two counter-monotonic random variables

Hanbali

Linders

Dhaene

2022

Scandinavian Actuarial Journal

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The Value-at-Risk (VaR) of comonotonic sums can be decomposed into marginal VaR's at the same level. This additivity property allows to derive useful decompositions for other risk measures. In particular, the Tail Value-at-Risk (TVaR) and the upper tail transform of comonotonic sums can be written as the sum of their corresponding marginal risk measures.The other extreme dependence situation, involving the sum of two arbitrary countermonotonic random variables, presents a certain number of challenges. One of them is that it is not straightforward to express the VaR of a counter-monotonic sum in terms of the VaR's of the marginal components of the sum. This paper generalizes the results derived in Chaoubi et al. (2020) by providing decomposition formulas for the VaR, TVaR and the stop-loss transform of the sum of two arbitrary counter-monotonic random variables.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%