An S-related DCV generated by a convex function in a jump market

Xiong, Dewen; Kohlmann, Michael

An S-related DCV generated by a convex function in a jump market

Dateien

Zu diesem Dokument gibt es keine Dateien.

Datum

2010

Autor:innen

Xiong, Dewen

Kohlmann, Michael

Publikationstyp

Zeitschriftenartikel

Publikationsstatus

Published

Erschienen in

Stochastic analysis and applications. 2010, 28(2), pp. 202-225. Available under: doi: 10.1080/07362990903546389

Zusammenfassung

We consider an incomplete market with general jumps, in which the discounted price process S of a risky asset is a given bounded semimartingale. We continue our work on the S-related dynamic convex valuation (DCV) initiated in Xiong and Kohlmann [23] by considering here an S-related DCV Cĝ whose dynamic penalty functional αĝ is generated by a convex function ĝ. So the penalty Junctional takes the following form is the density process of an equivalent martingale measure (EMM) Q for S with respect to the fundamental EMM Q0. For a given ∈ L∞ (FT), we prove that (Cĝ(ξ) is the first component of the minimal bounded solution of a backward semimartingale equation (BSE) generated by a convex, possibly non-Lipschitz g. If this BSE has a bounded solution (Y, θ1, θ2, L) such that θ2 is also bounded and 〈L〉T ∈ L∞ (FT), we prove that Cĝt(ξ) = Yt, Q0-a.s., for all t ∈ [0, T]. Finally, we introduce the concept of a bounded Cĝ-(super-)martingale and derive a decomposition for a Cĝ-supermartingale.

Fachgebiet (DDC)

510 Mathematik

Schlagwörter

Backward semimartingale equation (BSE), Dynamic convex risk measure, Dynamic convex valuation (DCV), Time-consistent property

Zitieren

ISO 690

XIONG, Dewen, Michael KOHLMANN, 2010. An S-related DCV generated by a convex function in a jump market. In: Stochastic analysis and applications. 2010, 28(2), pp. 202-225. Available under: doi: 10.1080/07362990903546389

BibTex

@article{Xiong2010Srela-835,
  year={2010},
  doi={10.1080/07362990903546389},
  title={An S-related DCV generated by a convex function in a jump market},
  number={2},
  volume={28},
  journal={Stochastic analysis and applications},
  pages={202--225},
  author={Xiong, Dewen and Kohlmann, Michael}
}

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/123456789/835">
    <dcterms:rights rdf:resource="https://rightsstatements.org/page/InC/1.0/"/>
    <dc:date rdf:datatype="http://www.w3.org/2001/XMLSchema#dateTime">2011-03-22T17:49:03Z</dc:date>
    <dcterms:bibliographicCitation>Publ. in: Stochastic analysis and applications 28 (2010), 2, pp. 202-225</dcterms:bibliographicCitation>
    <dc:language>eng</dc:language>
    <dc:creator>Xiong, Dewen</dc:creator>
    <dcterms:abstract xml:lang="eng">We consider an incomplete market with general jumps, in which the discounted price process S of a risky asset is a given bounded semimartingale. We continue our work on the S-related dynamic convex valuation (DCV) initiated in Xiong and Kohlmann [23] by considering here an S-related DCV Cĝ whose dynamic penalty functional αĝ is generated by a convex function ĝ. So the penalty Junctional takes the following form is the density process of an equivalent martingale measure (EMM) Q for S with respect to the fundamental EMM Q0. For a given ∈ L∞ (FT), we prove that (Cĝ(ξ) is the first component of the minimal bounded solution of a backward semimartingale equation (BSE) generated by a convex, possibly non-Lipschitz g. If this BSE has a bounded solution (Y, θ1, θ2, L) such that θ2 is also bounded and 〈L〉T ∈ L∞ (FT), we prove that Cĝt(ξ) = Yt, Q0-a.s., for all t ∈ [0, T]. Finally, we introduce the concept of a bounded Cĝ-(super-)martingale and derive a decomposition for a Cĝ-supermartingale.</dcterms:abstract>
    <void:sparqlEndpoint rdf:resource="http://localhost/fuseki/dspace/sparql"/>
    <dcterms:issued>2010</dcterms:issued>
    <dc:contributor>Kohlmann, Michael</dc:contributor>
    <bibo:uri rdf:resource="http://kops.uni-konstanz.de/handle/123456789/835"/>
    <dcterms:isPartOf rdf:resource="https://kops.uni-konstanz.de/server/rdf/resource/123456789/39"/>
    <dcterms:title>An S-related DCV generated by a convex function in a jump market</dcterms:title>
    <dc:contributor>Xiong, Dewen</dc:contributor>
    <foaf:homepage rdf:resource="http://localhost:8080/"/>
    <dspace:isPartOfCollection rdf:resource="https://kops.uni-konstanz.de/server/rdf/resource/123456789/39"/>
    <dcterms:available rdf:datatype="http://www.w3.org/2001/XMLSchema#dateTime">2011-03-22T17:49:03Z</dcterms:available>
    <dc:rights>terms-of-use</dc:rights>
    <dc:creator>Kohlmann, Michael</dc:creator>
  </rdf:Description>
</rdf:RDF>

Universitätsbibliographie

Ja