Type of Publication:  Journal article 
Publication status:  Published 
Author:  Delbaen, Freddy; Drapeau, Samuel; Kupper, Michael 
Year of publication:  2011 
Published in:  Journal of Mathematical Economics ; 47 (2011), 45.  pp. 401408.  ISSN 03044068.  eISSN 18731538 
DOI (citable link):  https://dx.doi.org/10.1016/j.jmateco.2011.04.002 
Summary: 
In the paradigm of von Neumann and Morgenstern (1947), a representation of affine preferences in terms of an expected utility can be obtained under the assumption of weak continuity. Since the weak topology is coarse, this requirement is a priori far from being negligible. In this work, we replace the assumption of weak continuity by monotonicity. More precisely, on the space of lotteries on an interval of the real line, it is shown that any affine preference order which is monotone with respect to the first stochastic order admits a representation in terms of an expected utility for some nondecreasing utility function. As a consequence, any affine preference order on the subset of lotteries with compact support, which is monotone with respect to the second stochastic order, can be represented in terms of an expected utility for some nondecreasing concave utility function. We also provide such representations for affine preference orders on the subset of those lotteries which fulfill some integrability conditions. The subtleties of the weak topology are illustrated by some examples.

Subject (DDC):  510 Mathematics 
Files  Size  Format  View 

There are no files associated with this item. 
DELBAEN, Freddy, Samuel DRAPEAU, Michael KUPPER, 2011. A von Neumann–Morgenstern representation result without weak continuity assumption. In: Journal of Mathematical Economics. 47(45), pp. 401408. ISSN 03044068. eISSN 18731538. Available under: doi: 10.1016/j.jmateco.2011.04.002
@article{Delbaen201108Neuma40951, title={A von Neumann–Morgenstern representation result without weak continuity assumption}, year={2011}, doi={10.1016/j.jmateco.2011.04.002}, number={45}, volume={47}, issn={03044068}, journal={Journal of Mathematical Economics}, pages={401408}, author={Delbaen, Freddy and Drapeau, Samuel and Kupper, Michael} }
<rdf:RDF xmlns:dcterms="http://purl.org/dc/terms/" xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:rdf="http://www.w3.org/1999/02/22rdfsyntaxns#" xmlns:bibo="http://purl.org/ontology/bibo/" xmlns:dspace="http://digitalrepositories.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.unikonstanz.de/rdf/resource/123456789/40951"> <dcterms:issued>201108</dcterms:issued> <void:sparqlEndpoint rdf:resource="http://localhost/fuseki/dspace/sparql"/> <foaf:homepage rdf:resource="http://localhost:8080/jspui"/> <dc:creator>Delbaen, Freddy</dc:creator> <dcterms:available rdf:datatype="http://www.w3.org/2001/XMLSchema#dateTime">20171215T13:27:08Z</dcterms:available> <dc:contributor>Drapeau, Samuel</dc:contributor> <dc:date rdf:datatype="http://www.w3.org/2001/XMLSchema#dateTime">20171215T13:27:08Z</dc:date> <dcterms:title>A von Neumann–Morgenstern representation result without weak continuity assumption</dcterms:title> <dcterms:abstract xml:lang="eng">In the paradigm of von Neumann and Morgenstern (1947), a representation of affine preferences in terms of an expected utility can be obtained under the assumption of weak continuity. Since the weak topology is coarse, this requirement is a priori far from being negligible. In this work, we replace the assumption of weak continuity by monotonicity. More precisely, on the space of lotteries on an interval of the real line, it is shown that any affine preference order which is monotone with respect to the first stochastic order admits a representation in terms of an expected utility for some nondecreasing utility function. As a consequence, any affine preference order on the subset of lotteries with compact support, which is monotone with respect to the second stochastic order, can be represented in terms of an expected utility for some nondecreasing concave utility function. We also provide such representations for affine preference orders on the subset of those lotteries which fulfill some integrability conditions. The subtleties of the weak topology are illustrated by some examples.</dcterms:abstract> <dspace:isPartOfCollection rdf:resource="https://kops.unikonstanz.de/rdf/resource/123456789/39"/> <dc:creator>Kupper, Michael</dc:creator> <dc:language>eng</dc:language> <dc:contributor>Kupper, Michael</dc:contributor> <bibo:uri rdf:resource="https://kops.unikonstanz.de/handle/123456789/40951"/> <dc:contributor>Delbaen, Freddy</dc:contributor> <dcterms:isPartOf rdf:resource="https://kops.unikonstanz.de/rdf/resource/123456789/39"/> <dc:creator>Drapeau, Samuel</dc:creator> </rdf:Description> </rdf:RDF>