Distortion risk measures of sums of two counter-monotonic risks

2025/03/07 by Huang, Chunle
#FOS: Economics and business #FOS: Mathematics #Mathematical Finance (q-fin.MF) #Probability (math.PR)

paper · doi:10.48550/arxiv.2503.05256

Abstract

In this paper, we will show that under certain conditions, associated to any fixed distortion function g, the distortion risk measure of a sum of two counter-monotonic risks can be expressed as the sum of two related distortion risk measures of the marginals involved, one associated to the original distortion function g and the other associated to the dual distortion function of g. This result extends some of the work in \citeChaoubi et al. (2020) and \citeHLD since the class of distortion risk measures includes the risk measure of VaR and TVaR as special cases.

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