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Risk exchange under infinite-mean Pareto models

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  • Yuyu Chen
  • Paul Embrechts
  • Ruodu Wang

Abstract

We study the optimal decisions 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. 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. The empirical studies show that extremely heavy tails exist in real datasets.

Suggested Citation

  • Yuyu Chen & Paul Embrechts & Ruodu Wang, 2024. "Risk exchange under infinite-mean Pareto models," Papers 2403.20171, arXiv.org.
    • Handle: RePEc:arx:papers:2403.20171
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    References listed on IDEAS

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