Characterizing a comonotonic random vector by the distribution of the sum of its components |
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Authors: | Ka Chun Cheung |
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Institution: | Department of Statistics and Actuarial Science, The University of Hong Kong, Pokfulam Road, Hong Kong |
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Abstract: | In this article, we characterize comonotonicity and related dependence structures among several random variables by the distribution of their sum. First we prove that if the sum has the same distribution as the corresponding comonotonic sum, then the underlying random variables must be comonotonic as long as each of them is integrable. In the literature, this result is only known to be true if either each random variable is square integrable or possesses a continuous distribution function. We then study the situation when the distribution of the sum only coincides with the corresponding comonotonic sum in the tail. This leads to the dependence structure known as tail comonotonicity. Finally, by establishing some new results concerning convex order, we show that comonotonicity can also be characterized by expected utility and distortion risk measures. |
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Keywords: | Convex order Stop-loss order Comonotonicity Distortion risk measure Distortion function |
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