Some remarks on the effect of risk sharing and diversification for infinite mean risks

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<title>Some remarks on the effect of risk sharing and diversification for infinite mean risks</title>
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<abstract displayLabel="Summary">Risk sharing is typically beneficial in insurance, but this can fail for heavy-tailed risks with infinite mean. In such cases, diversification may worsen outcomes a phenomenon known as the nondiversification trap, previously shown for stable, Pareto and Fréchet distributions. This paper demonstrates that the effect arises for any distribution more skewed than a Cauchy distribution and connects it to catastrophic risks with a positive probability of infinite loss, offering intuitive insight into why diversification can be harmful. Several open problems and conjectures related to these findings are also discussed</abstract>
<note type="statement of responsibility">Alfred Müller</note>
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<title>Astin bulletin</title>
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<publisher>Belgium : ASTIN and AFIR Sections of the International Actuarial Association</publisher>
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<identifier type="issn">0515-0361</identifier>
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<text>15/09/2025 Volume 55 Issue 3 - September 2025 , p. 747 - 756</text>
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