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We present simple general conditions on the acceptance sets under which theirinduced monetary risk and deviation measures are comonotonic additive. We showthat acceptance sets induce comonotonic additive risk measures if and only ifthe acceptance sets and their complements are stable under convex combinationsof comonotonic random variables. A generalization of this result applies torisk measures that are additive for random variables with a priori specifieddependence structures, e.g., perfectly correlated, uncorrelated, or independentrandom variables.

A note on the induction of comonotonic additive risk measures from acceptance sets