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A new proof of Cheung’s characterization of comonotonicity
Authors:Tiantian Mao Taizhong Hu
Institution:
  • Department of Statistics and Finance, School of Management, University of Science and Technology of China, Hefei, Anhui 230026, People’s Republic of China
  • Abstract:It is well known that if a random vector with given marginal distributions is comonotonic, it has the largest sum in the sense of the convex order. Cheung (2008) proved that the converse of this assertion is also true, provided that all marginal distribution functions are continuous and that the underlying probability space is atomless. This continuity assumption on the marginals was removed by Cheung (2010). In this short note, we give a new and simple proof of Cheung’s result without the assumption that the underlying probability space is atomless.
    Keywords:60E15
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