Characterizing mutual exclusivity as the strongest negative multivariate dependence structure |
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| Institution: | 1. Department of Statistics and Actuarial Science, University of Waterloo, Canada;2. Department of Mathematics and Statistics, University of Bern, Switzerland;1. Chair of Mathematical Finance, Technische Universität München, Parkring 11, 85748 Garching-Hochbrück, Germany;2. Institute of Mathematics – Business Mathematics, Universität Augsburg, Universitätsstraße 14, 86159 Augsburg, Germany;1. Department of Statistics and Finance, University of Science and Technology of China, Hefei, Anhui 230026, China;2. Department of Statistics and Actuarial Science, University of Waterloo, Waterloo, ON N2L3G1, Canada;1. Faculty of Business and Economics, Katholieke Universiteit Leuven, Belgium;2. Amsterdam School of Economics, University of Amsterdam, Netherlands;3. Department of Mathematics, Southern University of Science and Technology, China |
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| Abstract: | Mutual exclusivity is an extreme negative dependence structure that was first proposed and studied in Dhaene and Denuit (1999) in the context of insurance risks. In this article, we revisit this notion and present versatile characterizations of mutually exclusive random vectors via their pairwise counter-monotonic behaviour, minimal convex sum property, distributional representation and the characteristic function of the sum of their components. These characterizations highlight the role of mutual exclusivity in generalizing counter-monotonicity as the strongest negative dependence structure in a multi-dimensional setting. |
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| Keywords: | Mutual exclusivity Fréchet bounds Counter-monotonicity Convex order Complete mixability |
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