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arXiv · 2403.20171

Risk exchange under infinite-mean Pareto models

Yuyu Chen·Paul Embrechts·Ruodu Wang
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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.

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Yuyu Chen, Paul Embrechts, Ruodu Wang. 2024-03-24. Risk exchange under infinite-mean Pareto models. https://arxiv.org/abs/2403.20171

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