<oai_dc:dc xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:oai_dc="http://www.openarchives.org/OAI/2.0/oai_dc/" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:schemaLocation="http://www.openarchives.org/OAI/2.0/oai_dc/ http://www.openarchives.org/OAI/2.0/oai_dc.xsd">
  <dc:creator>Embrechts, Paul</dc:creator>
  <dc:creator>Wang, Ruodu</dc:creator>
  <dc:description xmlns:ns0="xml" ns0:lang="en">&lt;jats:title&gt;Abstract&lt;/jats:title&gt;&lt;jats:p&gt;Subadditivity is the key property which distinguishes the popular risk measures Value-at-Risk and
Expected Shortfall (ES). In this paper we offer seven proofs of the subadditivity of ES, some found in the literature
and some not. One of the main objectives of this paper is to provide a general guideline for instructors
to teach the subadditivity of ES in a course. We discuss the merits and suggest appropriate contexts for each
proof.With different proofs, different important properties of ES are revealed, such as its dual representation,
optimization properties, continuity, consistency with convex order, and natural estimators.&lt;/jats:p&gt;</dc:description>
  <dc:identifier>https://sonar.ch/global/documents/66550</dc:identifier>
  <dc:language>eng</dc:language>
  <dc:relation>info:eu-repo/semantics/altIdentifier/doi/10.1515/demo-2015-0009</dc:relation>
  <dc:relation>info:eu-repo/semantics/altIdentifier/issn/2300-2298</dc:relation>
  <dc:source>Dependence Modeling. - Walter de Gruyter GmbH. - 2015, vol. 3, no. 1</dc:source>
  <dc:title xmlns:ns1="xml" ns1:lang="en">Seven Proofs for the Subadditivity of Expected Shortfall</dc:title>
  <dc:type>http://purl.org/coar/resource_type/c_6501</dc:type>
</oai_dc:dc>