2023 Australasian Actuarial Education and Research Symposium

Yuyu Chen

University of Melbourne

Diversification of infinite-mean Pareto risks

This is joint work with Paul Embrechts, Ruodu Wang

We show the perhaps surprising inequality that the weighted average of i.i.d. extremely heavy-tailed (i.e., infinite mean) Pareto losses is larger than a standalone loss in the sense of first-order stochastic dominance. This result is further generalized to Pareto risks in the context of negative dependence, convex transformations, random summation and weights, and losses triggered by catastrophic events. We discuss several implications of these results via an equilibrium analysis in a risk exchange market. First, diversification of extremely heavy-tailed Pareto losses increases portfolio risk, and thus a diversification penalty exists. Second, agents with extremely heavy-tailed Pareto losses will not share risks in a market equilibrium. Third, transferring losses from agents bearing 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.