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


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

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

<rdf:RDF xmlns:dcterms="" xmlns:dc="" xmlns:rdf="" xmlns:bibo="" xmlns:dspace="" xmlns:foaf="" xmlns:void="" xmlns:xsd="" > <rdf:Description rdf:about=""> <dc:date rdf:datatype="">2011-03-22T17:49:03Z</dc:date> <dc:creator>Xiong, Dewen</dc:creator> <dcterms:issued>2010</dcterms:issued> <dc:language>eng</dc:language> <void:sparqlEndpoint rdf:resource="http://localhost/fuseki/dspace/sparql"/> <dc:contributor>Kohlmann, Michael</dc:contributor> <dc:creator>Kohlmann, Michael</dc:creator> <foaf:homepage rdf:resource="http://localhost:8080/jspui"/> <bibo:uri rdf:resource=""/> <dc:contributor>Xiong, Dewen</dc:contributor> <dcterms:title>An S-related DCV generated by a convex function in a jump market</dcterms:title> <dcterms:bibliographicCitation>Publ. in: Stochastic analysis and applications 28 (2010), 2, pp. 202-225</dcterms:bibliographicCitation> <dcterms:isPartOf rdf:resource=""/> <dcterms:available rdf:datatype="">2011-03-22T17:49:03Z</dcterms:available> <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> <dcterms:rights rdf:resource=""/> <dc:rights>terms-of-use</dc:rights> <dspace:isPartOfCollection rdf:resource=""/> </rdf:Description> </rdf:RDF>

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