Tail subadditivity of distortion risk measures and multivariate tail distortion risk measures

Jun Cai, Ying Wang and Tiantian Mao

Insurance: Mathematics and Economics, 2017, vol. 75, issue C, 105-116

Abstract: In this paper, we extend the concept of tail subadditivity (Belles-Sampera et al., 2014a; Belles-Sampera et al., 2014b) for distortion risk measures and give sufficient and necessary conditions for a distortion risk measure to be tail subadditive. We also introduce the generalized GlueVaR risk measures, which can be used to approach any coherent distortion risk measure. To further illustrate the applications of the tail subadditivity, we propose multivariate tail distortion (MTD) risk measures and generalize the multivariate tail conditional expectation (MTCE) risk measure introduced by Landsman et al. (2016). The properties of multivariate tail distortion risk measures, such as positive homogeneity, translation invariance, monotonicity, and subadditivity, are discussed as well. Moreover, we discuss the applications of the multivariate tail distortion risk measures in capital allocations for a portfolio of risks and explore the impacts of the dependence between risks in a portfolio and extreme tail events of a risk portfolio in capital allocations.

Keywords: Generalized GlueVaR; Subadditivity; Tail subadditivity; Tail distortion risk measure; Multivariate tail risk measure; Coherent risk measure; Choquet integral; Capital allocation (search for similar items in EconPapers)
Date: 2017
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Citations: View citations in EconPapers (11)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:insuma:v:75:y:2017:i:c:p:105-116

DOI: 10.1016/j.insmatheco.2017.05.004

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