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Risk exchange under infinite-mean Pareto models

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  • Chen, Yuyu
  • Embrechts, Paul
  • Wang, Ruodu

Abstract

We study the optimal decisions and equilibria of agents who aim to minimize their risks by allocating their positions over extremely heavy-tailed (i.e., infinite-mean) and possibly dependent losses. The loss distributions of our focus are super-Pareto distributions, which include the class of extremely heavy-tailed Pareto distributions. Using a recent result on stochastic dominance, we show that for a portfolio of super-Pareto losses, non-diversification is preferred by decision makers equipped with well-defined and monotone risk measures. The phenomenon that diversification is not beneficial in the presence of super-Pareto losses is further illustrated by an equilibrium analysis in a risk exchange market. First, agents with super-Pareto losses will not share risks in a market equilibrium. Second, transferring losses from agents bearing super-Pareto losses to external parties without any losses may arrive at an equilibrium which benefits every party involved.

Suggested Citation

  • Chen, Yuyu & Embrechts, Paul & Wang, Ruodu, 2025. "Risk exchange under infinite-mean Pareto models," Insurance: Mathematics and Economics, Elsevier, vol. 124(C).
    • Handle: RePEc:eee:insuma:v:124:y:2025:i:c:s0167668725000782
    DOI: 10.1016/j.insmatheco.2025.103131
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