Comonotonic Convex Preferences

This paper attempts to provide a decision-theoretic foundation for the measurement of economic tail risk, which is not only closely related to utility theory but also relevant to statistical model uncertainty. The main result is that the only risk measures that satisfy a set of economic axioms for the Choquet expected utility and the statistical property of elicitability (i.e. there exists an objective function such that minimizing the expected objective function yields the risk measure) are the mean functional and the median shortfall, which is the median of tail loss distribution. Elicitability is important for backtesting. We also extend the result to address model uncertainty by incorporating multiple scenarios. As an application, we argue that median shortfall is a better alternative than expected shortfall for setting capital requirements in Basel Accords.

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“…, 1/60, 0). The 9Gilboa and Schmeidler (1989) consider inf P ∈P u(X) dP without h i ; see alsoXia (2013).…”

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confidence: 99%

On the Measurement of Economic Tail Risk

Kou

Peng

2014

SSRN Journal

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“…. , n. The property of comonotonic quasiconvexity appeared in various contexts, e.g.,Xia (2013),Tian and Long (2015) andLi and Wang (2019).…”

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confidence: 99%

Cash-subadditive risk measures without quasi-convexity

Han

Wang

et al. 2021

Preprint

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In the literature of risk measures, cash subadditivity was proposed to replace cash additivity, motivated by the presence of stochastic or ambiguous interest rates and defaultable contingent claims. Cash subadditivity has been traditionally studied together with quasi-convexity, in a way similar to cash additivity with convexity. In this paper, we study cash-subadditive risk measures without quasi-convexity. One of our major results is that a general cash-subadditive risk measure can be represented as the lower envelope of a family of quasi-convex and cashsubadditive risk measures. Representation results of cash-subadditive risk measures with some additional common properties are also examined. We present an example where cash-subadditive risk measures naturally appear and discuss an application of the representation results of cashsubadditive risk measures to a risk sharing problem.

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Optimal Risk Sharing for Maxmin Choquet Expected Utility Model

Tian,

2024

Acta Math. Appl. Sin. Engl. Ser.

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Comonotonic Convex Preferences

Cited by 5 publications

References 37 publications

On the Measurement of Economic Tail Risk

On the Measurement of Economic Tail Risk

Cash-subadditive risk measures without quasi-convexity

Optimal Risk Sharing for Maxmin Choquet Expected Utility Model

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