VaR sub-additivity is impossible for one-sided risks except under co-monotonicity; super-additivity holds under negative simplex dependence and simplex dominance.
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VaR at Its Extremes: Impossibilities and Conditions for One-Sided Random Variables
VaR sub-additivity is impossible for one-sided risks except under co-monotonicity; super-additivity holds under negative simplex dependence and simplex dominance.