English

Distortion risk measures of sums of two counter-monotonic risks

Mathematical Finance 2025-03-10 v1 Probability

Abstract

In this paper, we will show that under certain conditions, associated to any fixed distortion function gg, 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 gg and the other associated to the dual distortion function of gg. This result extends some of the work in \cite{Chaoubi et al. (2020)} and \cite{HLD} since the class of distortion risk measures includes the risk measure of VaR and TVaR as special cases.

Keywords

Cite

@article{arxiv.2503.05256,
  title  = {Distortion risk measures of sums of two counter-monotonic risks},
  author = {Chunle Huang},
  journal= {arXiv preprint arXiv:2503.05256},
  year   = {2025}
}