  We show the perhaps surprising inequality that the weighted average of
negatively dependent super-Pareto random variables, possibly caused by
triggering events, is larger than one such random variable in the sense of
first-order stochastic dominance. The class of super-Pareto distributions is
extremely heavy-tailed and it includes the class of infinite-mean Pareto
distributions. We discuss several implications of this result via an
equilibrium analysis in a risk exchange market. First, diversification of
super-Pareto losses increases portfolio risk, and thus a diversification
penalty exists. Second, agents with super-Pareto losses will not share risks in
a market equilibrium. Third, transferring losses from agents bearing
super-Pareto losses to external parties without any losses may arrive at an
equilibrium which benefits every party involved. The empirical studies show
that our new inequality can be observed empirically for real datasets that fit
well with extremely heavy tails.

Risk Management;Theoretical Economics;Probability