Upper comonotonicity Cheung, Ka Chun

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Cheung, Ka Chun
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Insurance: Mathematics & Economics
Insurance; Mathematics; Business
To link to full-text access for this article, visit this link: http://dx.doi.org/10.1016/j.insmatheco.2009.03.003 Byline: Ka Chun Cheung Abstract: In this article, we study a new notion called upper comonotonicity, which is a generalization of the classical notion of comonotonicity. A random vector is upper-comonotonic if its components are moving in the same direction simultaneously when their values are greater than some thresholds. We provide a characterization of this new notion in terms of both the joint distribution function and the underlying copula. The copula characterization allows us to study the coefficient of upper tail dependence as well as the distributional representation of an upper-comonotonic random vector. As an application to financial economics, we show that the several commonly used risk measures, like the Value-at-Risk, the Tail Value-at-Risk, and the expected shortfall, are additive, not only for sum of comonotonic risks, but also for sum of upper-comonotonic risks, provided that the level of probability is greater than a certain threshold. Author Affiliation: Department of Statistics and Actuarial Science, The University of Hong Kong, Pokfulam Road, Hong Kong Article History: Received 11 November 2008; Revised 5 March 2009; Accepted 5 March 2009
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