Approaches to Conditional Risk

Filipović, Damir; Kupper, Michael; Vogelpoth, Nicolas

Approaches to Conditional Risk

Files

There are no files associated with this item.

Date

2012

Authors

Filipović, Damir

Kupper, Michael

Vogelpoth, Nicolas

DOI (citable link)

10.1137/090773076

Collections

Mathematik und Statistik

Publication type

Journal article

Publication status

Published

Published in

SIAM Journal on Financial Mathematics ; 3 (2012), 1. - pp. 402-432. - eISSN 1945-497X

Abstract

We present and compare two different approaches to conditional risk measures. One approach draws from convex analysis in vector spaces and presents risk measures as functions on $L^p$ spaces, while the other approach utilizes module-based convex analysis where conditional risk measures are defined on $L^p$-type modules. Both approaches utilize general duality theory for vector-valued convex functions, in contrast to the current literature, in which we find ad hoc dual representations. By presenting several applications such as monotone and (sub)cash invariant hulls with corresponding examples we illustrate that module-based convex analysis is well suited to the concept of conditional risk measures. Read More: http://epubs.siam.org/doi/abs/10.1137/090773076We present and compare two different approaches to conditional risk measures. One approach draws from convex analysis in vector spaces and presents risk measures as functions on $L^p$ spaces, while the other approach utilizes module-based convex analysis where conditional risk measures are defined on $L^p$-type modules. Both approaches utilize general duality theory for vector-valued convex functions, in contrast to the current literature, in which we find ad hoc dual representations. By presenting several applications such as monotone and (sub)cash invariant hulls with corresponding examples we illustrate that module-based convex analysis is well suited to the concept of conditional risk measures.

Subject (DDC)

510 Mathematics

Cite This

ISO 690

FILIPOVIĆ, Damir, Michael KUPPER, Nicolas VOGELPOTH, 2012. Approaches to Conditional Risk. In: SIAM Journal on Financial Mathematics. 3(1), pp. 402-432. eISSN 1945-497X. Available under: doi: 10.1137/090773076

BibTex

@article{Filipovic2012-01Appro-40916,
  year={2012},
  doi={10.1137/090773076},
  title={Approaches to Conditional Risk},
  number={1},
  volume={3},
  journal={SIAM Journal on Financial Mathematics},
  pages={402--432},
  author={Filipović, Damir and Kupper, Michael and Vogelpoth, Nicolas}
}

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/123456789/40916">
    <dc:contributor>Filipović, Damir</dc:contributor>
    <dc:creator>Vogelpoth, Nicolas</dc:creator>
    <dcterms:abstract xml:lang="eng">We present and compare two different approaches to conditional risk measures. One approach draws from convex analysis in vector spaces and presents risk measures as functions on $L^p$ spaces, while the other approach utilizes module-based convex analysis where conditional risk measures are defined on $L^p$-type modules. Both approaches utilize general duality theory for vector-valued convex functions, in contrast to the current literature, in which we find ad hoc dual representations. By presenting several applications such as monotone and (sub)cash invariant hulls with corresponding examples we illustrate that module-based convex analysis is well suited to the concept of conditional risk measures. Read More: http://epubs.siam.org/doi/abs/10.1137/090773076We present and compare two different approaches to conditional risk measures. One approach draws from convex analysis in vector spaces and presents risk measures as functions on $L^p$ spaces, while the other approach utilizes module-based convex analysis where conditional risk measures are defined on $L^p$-type modules. Both approaches utilize general duality theory for vector-valued convex functions, in contrast to the current literature, in which we find ad hoc dual representations. By presenting several applications such as monotone and (sub)cash invariant hulls with corresponding examples we illustrate that module-based convex analysis is well suited to the concept of conditional risk measures.</dcterms:abstract>
    <dc:creator>Filipović, Damir</dc:creator>
    <dcterms:isPartOf rdf:resource="https://kops.uni-konstanz.de/server/rdf/resource/123456789/39"/>
    <dc:creator>Kupper, Michael</dc:creator>
    <dspace:isPartOfCollection rdf:resource="https://kops.uni-konstanz.de/server/rdf/resource/123456789/39"/>
    <bibo:uri rdf:resource="https://kops.uni-konstanz.de/handle/123456789/40916"/>
    <foaf:homepage rdf:resource="http://localhost:8080/"/>
    <void:sparqlEndpoint rdf:resource="http://localhost/fuseki/dspace/sparql"/>
    <dc:contributor>Kupper, Michael</dc:contributor>
    <dcterms:available rdf:datatype="http://www.w3.org/2001/XMLSchema#dateTime">2017-12-13T10:49:55Z</dcterms:available>
    <dcterms:title>Approaches to Conditional Risk</dcterms:title>
    <dc:contributor>Vogelpoth, Nicolas</dc:contributor>
    <dc:language>eng</dc:language>
    <dcterms:issued>2012-01</dcterms:issued>
    <dc:date rdf:datatype="http://www.w3.org/2001/XMLSchema#dateTime">2017-12-13T10:49:55Z</dc:date>
  </rdf:Description>
</rdf:RDF>

Bibliography of Konstanz

No