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

<?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:schemaLocation="http://www.loc.gov/MARC21/slim http://www.loc.gov/standards/marcxml/schema/MARC21slim.xsd">
  <record>
    <leader>00000cab a2200000   4500</leader>
    <controlfield tag="001">MAP20260001937</controlfield>
    <controlfield tag="003">MAP</controlfield>
    <controlfield tag="005">20260202114506.0</controlfield>
    <controlfield tag="008">260202e20250915bel|||p      |0|||b|eng d</controlfield>
    <datafield tag="040" ind1=" " ind2=" ">
      <subfield code="a">MAP</subfield>
      <subfield code="b">spa</subfield>
      <subfield code="d">MAP</subfield>
    </datafield>
    <datafield tag="084" ind1=" " ind2=" ">
      <subfield code="a">6</subfield>
    </datafield>
    <datafield tag="100" ind1=" " ind2=" ">
      <subfield code="0">MAPA20080109554</subfield>
      <subfield code="a">Müller, Alfred</subfield>
    </datafield>
    <datafield tag="245" ind1="1" ind2="0">
      <subfield code="a">Some remarks on the effect of risk sharing and diversification for infinite mean risks</subfield>
      <subfield code="c">Alfred Müller</subfield>
    </datafield>
    <datafield tag="520" ind1=" " ind2=" ">
      <subfield code="a">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</subfield>
    </datafield>
    <datafield tag="650" ind1=" " ind2="4">
      <subfield code="0">MAPA20080610319</subfield>
      <subfield code="a">Distribución de riesgos</subfield>
    </datafield>
    <datafield tag="650" ind1=" " ind2="4">
      <subfield code="0">MAPA20260001562</subfield>
      <subfield code="a">Riesgos catastróficos</subfield>
    </datafield>
    <datafield tag="650" ind1=" " ind2="4">
      <subfield code="0">MAPA20080625542</subfield>
      <subfield code="a">Diversificación de los riesgos</subfield>
    </datafield>
    <datafield tag="650" ind1=" " ind2="4">
      <subfield code="0">MAPA20080586294</subfield>
      <subfield code="a">Mercado de seguros</subfield>
    </datafield>
    <datafield tag="650" ind1=" " ind2="4">
      <subfield code="0">MAPA20080579258</subfield>
      <subfield code="a">Cálculo actuarial</subfield>
    </datafield>
    <datafield tag="650" ind1=" " ind2="4">
      <subfield code="0">MAPA20080592042</subfield>
      <subfield code="a">Modelos matemáticos</subfield>
    </datafield>
    <datafield tag="650" ind1=" " ind2="4">
      <subfield code="0">MAPA20090033023</subfield>
      <subfield code="a">Estadística matemática</subfield>
    </datafield>
    <datafield tag="710" ind1="2" ind2=" ">
      <subfield code="0">MAPA20100017661</subfield>
      <subfield code="a">International Actuarial Association</subfield>
    </datafield>
    <datafield tag="773" ind1="0" ind2=" ">
      <subfield code="w">MAP20077000420</subfield>
      <subfield code="g">15/09/2025 Volume 55 Issue 3 - September 2025 , p. 747 - 756</subfield>
      <subfield code="x">0515-0361</subfield>
      <subfield code="t">Astin bulletin</subfield>
      <subfield code="d">Belgium : ASTIN and AFIR Sections of the International Actuarial Association</subfield>
    </datafield>
  </record>
</collection>