Type of Publication:  Journal article 
Publication status:  Published 
Author:  Bartl, Daniel; Drapeau, Samuel; Tangpi, Ludovic 
Year of publication:  2020 
Published in:  Mathematical Finance ; 30 (2020), 1.  pp. 287309.  Wiley.  ISSN 09601627.  eISSN 14679965 
DOI (citable link):  https://dx.doi.org/10.1111/mafi.12203 
Summary: 
Accounting for model uncertainty in risk management and option pricing leads to infinite‐dimensional optimization problems that are both analytically and numerically intractable. In this article, we study when this hurdle can be overcome for the so‐called optimized certainty equivalent (OCE) risk measure—including the average value‐at‐risk as a special case. First, we focus on the case where the uncertainty is modeled by a nonlinear expectation that penalizes distributions that are “far” in terms of optimal‐transport distance (e.g. Wasserstein distance) from a given baseline distribution. It turns out that the computation of the robust OCE reduces to a finite‐dimensional problem, which in some cases can even be solved explicitly. This principle also applies to the shortfall risk measure as well as for the pricing of European options. Further, we derive convex dual representations of the robust OCE for measurable claims without any assumptions on the set of distributions. Finally, we give conditions on the latter set under which the robust average value‐at‐risk is a tail risk measure.

Subject (DDC):  510 Mathematics 
Keywords:  average valueatrisk, convex duality, distribution uncertainty, optimized certainty equivalent, optimal transport, penalization, robust option pricing, Wasserstein distance 
Refereed:  Yes 
Files  Size  Format  View 

There are no files associated with this item. 
BARTL, Daniel, Samuel DRAPEAU, Ludovic TANGPI, 2020. Computational aspects of robust optimized certainty equivalents and option pricing. In: Mathematical Finance. Wiley. 30(1), pp. 287309. ISSN 09601627. eISSN 14679965. Available under: doi: 10.1111/mafi.12203
@article{Bartl202001Compu48304, title={Computational aspects of robust optimized certainty equivalents and option pricing}, year={2020}, doi={10.1111/mafi.12203}, number={1}, volume={30}, issn={09601627}, journal={Mathematical Finance}, pages={287309}, author={Bartl, Daniel and Drapeau, Samuel and Tangpi, Ludovic} }
<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/123456789/48304"> <dspace:isPartOfCollection rdf:resource="https://kops.unikonstanz.de/rdf/resource/123456789/39"/> <dc:creator>Bartl, Daniel</dc:creator> <dc:creator>Drapeau, Samuel</dc:creator> <dcterms:title>Computational aspects of robust optimized certainty equivalents and option pricing</dcterms:title> <dc:contributor>Tangpi, Ludovic</dc:contributor> <bibo:uri rdf:resource="https://kops.unikonstanz.de/handle/123456789/48304"/> <dcterms:issued>202001</dcterms:issued> <dc:contributor>Drapeau, Samuel</dc:contributor> <dc:language>eng</dc:language> <dc:creator>Tangpi, Ludovic</dc:creator> <dc:date rdf:datatype="http://www.w3.org/2001/XMLSchema#dateTime">20200121T10:52:40Z</dc:date> <dcterms:available rdf:datatype="http://www.w3.org/2001/XMLSchema#dateTime">20200121T10:52:40Z</dcterms:available> <dc:contributor>Bartl, Daniel</dc:contributor> <foaf:homepage rdf:resource="http://localhost:8080/jspui"/> <dcterms:abstract xml:lang="eng">Accounting for model uncertainty in risk management and option pricing leads to infinite‐dimensional optimization problems that are both analytically and numerically intractable. In this article, we study when this hurdle can be overcome for the so‐called optimized certainty equivalent (OCE) risk measure—including the average value‐at‐risk as a special case. First, we focus on the case where the uncertainty is modeled by a nonlinear expectation that penalizes distributions that are “far” in terms of optimal‐transport distance (e.g. Wasserstein distance) from a given baseline distribution. It turns out that the computation of the robust OCE reduces to a finite‐dimensional problem, which in some cases can even be solved explicitly. This principle also applies to the shortfall risk measure as well as for the pricing of European options. Further, we derive convex dual representations of the robust OCE for measurable claims without any assumptions on the set of distributions. Finally, we give conditions on the latter set under which the robust average value‐at‐risk is a tail risk measure.</dcterms:abstract> <void:sparqlEndpoint rdf:resource="http://localhost/fuseki/dspace/sparql"/> <dcterms:isPartOf rdf:resource="https://kops.unikonstanz.de/rdf/resource/123456789/39"/> </rdf:Description> </rdf:RDF>