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

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  • Alfred Muller

Abstract

The basic principle of any version of insurance is the paradigm that exchanging risk by sharing it in a pool is beneficial for the participants. In case of independent risks with a finite mean this is the case for risk averse decision makers. The situation may be very different in case of infinite mean models. In that case it is known that risk sharing may have a negative effect, which is sometimes called the nondiversification trap. This phenomenon is well known for infinite mean stable distributions. In a series of recent papers similar results for infinite mean Pareto and Fr\'echet distributions have been obtained. We further investigate this property by showing that many of these results can be obtained as special cases of a simple result demonstrating that this holds for any distribution that is more skewed than a Cauchy distribution. We also relate this to the situation of deadly catastrophic risks, where we assume a positive probability for an infinite value. That case gives a very simple intuition why this phenomenon can occur for such catastrophic risks. We also mention several open problems and conjectures in this context.

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  • Alfred Muller, 2024. "Some remarks on the effect of risk sharing and diversification for infinite mean risks," Papers 2411.10139, arXiv.org.
  • Handle: RePEc:arx:papers:2411.10139
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    1. Rustam Ibragimov & Dwight Jaffee & Johan Walden, 2009. "Nondiversification Traps in Catastrophe Insurance Markets," The Review of Financial Studies, Society for Financial Studies, vol. 22(3), pages 959-993, March.
    2. Yuyu Chen & Paul Embrechts & Ruodu Wang, 2024. "Risk exchange under infinite-mean Pareto models," Papers 2403.20171, arXiv.org.
    3. Eugene F. Fama, 1965. "Portfolio Analysis in a Stable Paretian Market," Management Science, INFORMS, vol. 11(3), pages 404-419, January.
    4. Rustam Ibragimov & Dwight Jaffee & Johan Walden, 2009. "Nondiversification Traps in Catastrophe Insurance Markets," The Review of Financial Studies, Society for Financial Studies, vol. 22(3), pages 959-993.
    5. Eling, Martin & Wirfs, Jan, 2019. "What are the actual costs of cyber risk events?," European Journal of Operational Research, Elsevier, vol. 272(3), pages 1109-1119.
    6. Yuyu Chen & Paul Embrechts & Ruodu Wang, 2022. "An unexpected stochastic dominance: Pareto distributions, dependence, and diversification," Papers 2208.08471, arXiv.org, revised Mar 2024.
    7. Runhuan Feng & Chongda Liu & Stephen Taylor, 2023. "Peer-to-peer risk sharing with an application to flood risk pooling," Annals of Operations Research, Springer, vol. 321(1), pages 813-842, February.
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