Type of Publication:  Journal article 
Publication status:  Published 
URI (citable link):  http://nbnresolving.de/urn:nbn:de:bsz:352217wvsj60byn202 
Author:  Eckstein, Stephan; Kupper, Michael; Pohl, Mathias 
Year of publication:  2020 
Published in:  Mathematical Finance ; 30 (2020), 4.  pp. 12291272.  Wiley.  ISSN 09601627.  eISSN 14679965 
Pubmed ID:  33041536 
DOI (citable link):  https://dx.doi.org/10.1111/mafi.12280 
Summary: 
We consider settings in which the distribution of a multivariate random variable is partly ambiguous. We assume the ambiguity lies on the level of the dependence structure, and that the marginal distributions are known. Furthermore, a current best guess for the distribution, called reference measure, is available. We work with the set of distributions that are both close to the given reference measure in a transportation distance (e.g., the Wasserstein distance), and additionally have the correct marginal structure. The goal is to find upper and lower bounds for integrals of interest with respect to distributions in this set. The described problem appears naturally in the context of risk aggregation. When aggregating different risks, the marginal distributions of these risks are known and the task is to quantify their joint effect on a given system. This is typically done by applying a meaningful risk measure to the sum of the individual risks. For this purpose, the stochastic interdependencies between the risks need to be specified. In practice, the models of this dependence structure are however subject to relatively high model ambiguity. The contribution of this paper is twofold: First, we derive a dual representation of the considered problem and prove that strong duality holds. Second, we propose a generally applicable and computationally feasible method, which relies on neural networks, in order to numerically solve the derived dual problem. The latter method is tested on a number of toy examples, before it is finally applied to perform robust risk aggregation in a real‐world instance.

Subject (DDC):  510 Mathematics 
Link to License:  Attribution 4.0 International 
Bibliography of Konstanz:  Yes 
Refereed:  Yes 
ECKSTEIN, Stephan, Michael KUPPER, Mathias POHL, 2020. Robust risk aggregation with neural networks. In: Mathematical Finance. Wiley. 30(4), pp. 12291272. ISSN 09601627. eISSN 14679965. Available under: doi: 10.1111/mafi.12280
@article{Eckstein202010Robus50084, title={Robust risk aggregation with neural networks}, year={2020}, doi={10.1111/mafi.12280}, number={4}, volume={30}, issn={09601627}, journal={Mathematical Finance}, pages={12291272}, author={Eckstein, Stephan and Kupper, Michael and Pohl, Mathias} }
<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/123456789/50084"> <dc:contributor>Eckstein, Stephan</dc:contributor> <dc:language>eng</dc:language> <dc:date rdf:datatype="http://www.w3.org/2001/XMLSchema#dateTime">20200701T11:25:38Z</dc:date> <dcterms:available rdf:datatype="http://www.w3.org/2001/XMLSchema#dateTime">20200701T11:25:38Z</dcterms:available> <dcterms:issued>202010</dcterms:issued> <dc:creator>Eckstein, Stephan</dc:creator> <void:sparqlEndpoint rdf:resource="http://localhost/fuseki/dspace/sparql"/> <dcterms:abstract xml:lang="eng">We consider settings in which the distribution of a multivariate random variable is partly ambiguous. We assume the ambiguity lies on the level of the dependence structure, and that the marginal distributions are known. Furthermore, a current best guess for the distribution, called reference measure, is available. We work with the set of distributions that are both close to the given reference measure in a transportation distance (e.g., the Wasserstein distance), and additionally have the correct marginal structure. The goal is to find upper and lower bounds for integrals of interest with respect to distributions in this set. The described problem appears naturally in the context of risk aggregation. When aggregating different risks, the marginal distributions of these risks are known and the task is to quantify their joint effect on a given system. This is typically done by applying a meaningful risk measure to the sum of the individual risks. For this purpose, the stochastic interdependencies between the risks need to be specified. In practice, the models of this dependence structure are however subject to relatively high model ambiguity. The contribution of this paper is twofold: First, we derive a dual representation of the considered problem and prove that strong duality holds. Second, we propose a generally applicable and computationally feasible method, which relies on neural networks, in order to numerically solve the derived dual problem. The latter method is tested on a number of toy examples, before it is finally applied to perform robust risk aggregation in a real‐world instance.</dcterms:abstract> <dcterms:title>Robust risk aggregation with neural networks</dcterms:title> <dcterms:hasPart rdf:resource="https://kops.unikonstanz.de/bitstream/123456789/50084/1/Eckstein_217wvsj60byn202.pdf"/> <foaf:homepage rdf:resource="http://localhost:8080/jspui"/> <dc:contributor>Kupper, Michael</dc:contributor> <dspace:isPartOfCollection rdf:resource="https://kops.unikonstanz.de/rdf/resource/123456789/39"/> <dcterms:isPartOf rdf:resource="https://kops.unikonstanz.de/rdf/resource/123456789/39"/> <dc:creator>Pohl, Mathias</dc:creator> <bibo:uri rdf:resource="https://kops.unikonstanz.de/handle/123456789/50084"/> <dspace:hasBitstream rdf:resource="https://kops.unikonstanz.de/bitstream/123456789/50084/1/Eckstein_217wvsj60byn202.pdf"/> <dc:creator>Kupper, Michael</dc:creator> <dcterms:rights rdf:resource="http://creativecommons.org/licenses/by/4.0/"/> <dc:rights>Attribution 4.0 International</dc:rights> <dc:contributor>Pohl, Mathias</dc:contributor> </rdf:Description> </rdf:RDF>
Eckstein_217wvsj60byn202.pdf  28 