On a class of law invariant convex risk measures

Angelsberg, Gilles; Delbaen, Freddy; Kaelin, Ivo; Kupper, Michael; Näf, Joachim

On a class of law invariant convex risk measures

Dateien

Zu diesem Dokument gibt es keine Dateien.

Datum

2011

Autor:innen

Angelsberg, Gilles

Delbaen, Freddy

Kaelin, Ivo

Kupper, Michael

Näf, Joachim

DOI (zitierfähiger Link)

https://doi.org/10.1007/s00780-010-0145-5

Sammlungen

Mathematik und Statistik

Publikationstyp

Zeitschriftenartikel

Publikationsstatus

Published

Erschienen in

Finance and Stochastics. Springer. 2011, 15, pp. 343-363. ISSN 0949-2984. eISSN 1432-1122. Available under: doi: 10.1007/s00780-010-0145-5

Zusammenfassung

We consider the class of law invariant convex risk measures with robust representation ρ_h,p(X)=sup_f∫¹₀[AV@R_s(X)f(s)−f^p(s)h(s)]ds, where 1≤p<∞ and h is a positive and strictly decreasing function. The supremum is taken over the set of all Radon–Nikodým derivatives corresponding to the set of all probability measures on (0,1] which are absolutely continuous with respect to Lebesgue measure. We provide necessary and sufficient conditions for the position X such that ρ _h,p(X) is real-valued and the supremum is attained. Using variational methods, an explicit formula for the maximizer is given. We exhibit two examples of such risk measures and compare them to the average value at risk.

Fachgebiet (DDC)

510 Mathematik

Zitieren

ISO 690

ANGELSBERG, Gilles, Freddy DELBAEN, Ivo KAELIN, Michael KUPPER, Joachim NÄF, 2011. On a class of law invariant convex risk measures. In: Finance and Stochastics. Springer. 2011, 15, pp. 343-363. ISSN 0949-2984. eISSN 1432-1122. Available under: doi: 10.1007/s00780-010-0145-5

BibTex

@article{Angelsberg2011class-55458,
  year={2011},
  doi={10.1007/s00780-010-0145-5},
  title={On a class of law invariant convex risk measures},
  volume={15},
  issn={0949-2984},
  journal={Finance and Stochastics},
  pages={343--363},
  author={Angelsberg, Gilles and Delbaen, Freddy and Kaelin, Ivo and Kupper, Michael and Näf, Joachim}
}

RDF

<rdf:RDF
    xmlns:dcterms="http://purl.org/dc/terms/"
    xmlns:dc="http://purl.org/dc/elements/1.1/"
    xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
    xmlns:bibo="http://purl.org/ontology/bibo/"
    xmlns:dspace="http://digital-repositories.org/ontologies/dspace/0.1.0#"
    xmlns:foaf="http://xmlns.com/foaf/0.1/"
    xmlns:void="http://rdfs.org/ns/void#"
    xmlns:xsd="http://www.w3.org/2001/XMLSchema#" > 
  <rdf:Description rdf:about="https://kops.uni-konstanz.de/server/rdf/resource/123456789/55458">
    <dc:creator>Angelsberg, Gilles</dc:creator>
    <dc:creator>Kaelin, Ivo</dc:creator>
    <dc:contributor>Kupper, Michael</dc:contributor>
    <dc:contributor>Kaelin, Ivo</dc:contributor>
    <dc:creator>Kupper, Michael</dc:creator>
    <dc:rights>terms-of-use</dc:rights>
    <dcterms:available rdf:datatype="http://www.w3.org/2001/XMLSchema#dateTime">2021-11-08T08:59:09Z</dcterms:available>
    <dc:language>eng</dc:language>
    <dc:creator>Delbaen, Freddy</dc:creator>
    <dc:contributor>Näf, Joachim</dc:contributor>
    <foaf:homepage rdf:resource="http://localhost:8080/"/>
    <dcterms:isPartOf rdf:resource="https://kops.uni-konstanz.de/server/rdf/resource/123456789/39"/>
    <dspace:isPartOfCollection rdf:resource="https://kops.uni-konstanz.de/server/rdf/resource/123456789/39"/>
    <dc:date rdf:datatype="http://www.w3.org/2001/XMLSchema#dateTime">2021-11-08T08:59:09Z</dc:date>
    <dc:contributor>Angelsberg, Gilles</dc:contributor>
    <dcterms:abstract xml:lang="eng">We consider the class of law invariant convex risk measures with robust representation ρ&lt;sub&gt;h,p&lt;/sub&gt;(X)=sup&lt;sub&gt;f&lt;/sub&gt;∫&lt;sup&gt;1&lt;/sup&gt;&lt;sub&gt;0&lt;/sub&gt;[AV@R&lt;sub&gt;s&lt;/sub&gt;(X)f(s)−f&lt;sup&gt;p&lt;/sup&gt;(s)h(s)]ds, where 1≤p&lt;∞ and h is a positive and strictly decreasing function. The supremum is taken over the set of all Radon–Nikodým derivatives corresponding to the set of all probability measures on (0,1] which are absolutely continuous with respect to Lebesgue measure. We provide necessary and sufficient conditions for the position X such that ρ &lt;sub&gt;h,p&lt;/sub&gt;(X) is real-valued and the supremum is attained. Using variational methods, an explicit formula for the maximizer is given. We exhibit two examples of such risk measures and compare them to the average value at risk.</dcterms:abstract>
    <dcterms:issued>2011</dcterms:issued>
    <dc:contributor>Delbaen, Freddy</dc:contributor>
    <dc:creator>Näf, Joachim</dc:creator>
    <void:sparqlEndpoint rdf:resource="http://localhost/fuseki/dspace/sparql"/>
    <dcterms:rights rdf:resource="https://rightsstatements.org/page/InC/1.0/"/>
    <dcterms:title>On a class of law invariant convex risk measures</dcterms:title>
    <bibo:uri rdf:resource="https://kops.uni-konstanz.de/handle/123456789/55458"/>
  </rdf:Description>
</rdf:RDF>

Universitätsbibliographie

Nein

Begutachtet

Ja