Centro de Documentacion de Fundación MAPFRE - Some remarks on the effect of risk sharing and diversification for infinite mean risks

Notes: Sumario: 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 discussedRelated records: En: Astin bulletin. - Belgium : ASTIN and AFIR Sections of the International Actuarial Association = ISSN 0515-0361. - 15/09/2025 Volume 55 Issue 3 - September 2025 , p. 747 - 756Materia / lugar / evento: Distribución de riesgos Riesgos catastróficos Diversificación de los riesgos Mercado de seguros Cálculo actuarial Modelos matemáticos Estadística matemática Otros autores: International Actuarial Association
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