A Note on continuity and asymptotic consistency of measures of risk and variability

<?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">MAP20260001555</controlfield>
    <controlfield tag="003">MAP</controlfield>
    <controlfield tag="005">20260129112613.0</controlfield>
    <controlfield tag="008">260129e20250129bel|||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="1" ind2=" ">
      <subfield code="0">MAPA20260001043</subfield>
      <subfield code="a">Gao, Niushan</subfield>
    </datafield>
    <datafield tag="245" ind1="1" ind2="2">
      <subfield code="a">A Note on continuity and asymptotic consistency of measures of risk and variability</subfield>
      <subfield code="c">Niushan Gao and Foivos Xanthos</subfield>
    </datafield>
    <datafield tag="520" ind1=" " ind2=" ">
      <subfield code="a">They show that every convex, order-bounded above functional on a Fréchet lattice is automatically continuous. This improves a result in Ruszczynski and Shapiro ((2006) Mathematics of Operations Research 31(3), 433452.) and applies to many deviation and variability measures. We also show that an order-continuous, law-invariant functional on an Orlicz space is strongly consistent everywhere, extending a result in Krätschmer et al (2017) Finance and Stochastics 18(2), 271295)</subfield>
    </datafield>
    <datafield tag="650" ind1=" " ind2="4">
      <subfield code="0">MAPA20080602437</subfield>
      <subfield code="a">Matemática del seguro</subfield>
    </datafield>
    <datafield tag="650" ind1=" " ind2="4">
      <subfield code="0">MAPA20080604721</subfield>
      <subfield code="a">Análisis multivariante</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">MAPA20080574871</subfield>
      <subfield code="a">Cálculo integral</subfield>
    </datafield>
    <datafield tag="700" ind1="1" ind2=" ">
      <subfield code="0">MAPA20260001050</subfield>
      <subfield code="a">Xanthos, Foivos </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">29/01/2025 Volume 55 Issue 1 - January 2025 , p. 168-177</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>