Coherent measures of risk defined by the axioms of monotonicity, subadditivity, positive homogeneity, and translation invariance are recent tools in risk management to assess the amount of risk agents are exposed to. If they also satisfy law invariance and comonotonic additivity, then we get a...

Measuring risk can be axiomatized by the concept of coherent measures of risk. A risk environment specifies some individual portfolios' realization vectors and a coherent measure of risk. We consider sharing the risk of the aggregate portfolio by studying transferable utility cooperative games:...