{"id":"https://openalex.org/W2886098351","doi":"https://doi.org/10.1137/21m144709x","title":"Marginal and Dependence Uncertainty: Bounds, Optimal Transport, and Sharpness","display_name":"Marginal and Dependence Uncertainty: Bounds, Optimal Transport, and Sharpness","publication_year":2022,"publication_date":"2022-02-01","ids":{"openalex":"https://openalex.org/W2886098351","doi":"https://doi.org/10.1137/21m144709x","mag":"2886098351"},"language":"en","primary_location":{"id":"doi:10.1137/21m144709x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/21m144709x","pdf_url":null,"source":{"id":"https://openalex.org/S897311980","display_name":"SIAM Journal on Control and Optimization","issn_l":"0363-0129","issn":["0363-0129","1095-7138"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Control and Optimization","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1709.00641","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5037788262","display_name":"Daniel Bartl","orcid":"https://orcid.org/0000-0002-1379-2401"},"institutions":[{"id":"https://openalex.org/I129774422","display_name":"University of Vienna","ror":"https://ror.org/03prydq77","country_code":"AT","type":"education","lineage":["https://openalex.org/I129774422"]},{"id":"https://openalex.org/I159176309","display_name":"Universit\u00e4t Hamburg","ror":"https://ror.org/00g30e956","country_code":"DE","type":"education","lineage":["https://openalex.org/I159176309"]},{"id":"https://openalex.org/I189712700","display_name":"University of Konstanz","ror":"https://ror.org/0546hnb39","country_code":"DE","type":"education","lineage":["https://openalex.org/I189712700"]},{"id":"https://openalex.org/I4210127348","display_name":"FORTH Institute of Electronic Structure and Laser","ror":"https://ror.org/02a3mhk13","country_code":"GR","type":"facility","lineage":["https://openalex.org/I4210127348","https://openalex.org/I8901234"]},{"id":"https://openalex.org/I4210160622","display_name":"Helsana Group (Switzerland)","ror":"https://ror.org/0530gr416","country_code":"CH","type":"company","lineage":["https://openalex.org/I4210160622"]},{"id":"https://openalex.org/I98358874","display_name":"Delft University of Technology","ror":"https://ror.org/02e2c7k09","country_code":"NL","type":"education","lineage":["https://openalex.org/I98358874"]}],"countries":["AT","CH","DE","GR","NL"],"is_corresponding":false,"raw_author_name":"Daniel Bartl","raw_affiliation_strings":["\\P Delft Institute of Applied Mathematics, TU Delft, 2628 Delft, The Netherlands, and Institute of Applied and Computational Mathematics,","\\dagger Faculty of Mathematics, University of Vienna, 1090, Vienna, Austria","\\ddagger Department of Mathematics, University of Konstanz, 78464, Konstanz, Germany","\\| Department of Mathematics, University of Hamburg, 20146, Hamburg, Germany","\\S Group Actuarial Department, Helvetia Insurance Group, 9001, St. Gallen, Switzerland","FORTH, 70013, Heraklion, Greece"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"\\P Delft Institute of Applied Mathematics, TU Delft, 2628 Delft, The Netherlands, and Institute of Applied and Computational Mathematics,","institution_ids":["https://openalex.org/I98358874"]},{"raw_affiliation_string":"\\dagger Faculty of Mathematics, University of Vienna, 1090, Vienna, Austria","institution_ids":["https://openalex.org/I129774422"]},{"raw_affiliation_string":"\\ddagger Department of Mathematics, University of Konstanz, 78464, Konstanz, Germany","institution_ids":["https://openalex.org/I189712700"]},{"raw_affiliation_string":"\\| Department of Mathematics, University of Hamburg, 20146, Hamburg, Germany","institution_ids":["https://openalex.org/I159176309"]},{"raw_affiliation_string":"\\S Group Actuarial Department, Helvetia Insurance Group, 9001, St. Gallen, Switzerland","institution_ids":["https://openalex.org/I4210160622"]},{"raw_affiliation_string":"FORTH, 70013, Heraklion, Greece","institution_ids":["https://openalex.org/I4210127348"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5089523092","display_name":"Michael Kupper","orcid":"https://orcid.org/0000-0001-9643-0811"},"institutions":[{"id":"https://openalex.org/I129774422","display_name":"University of Vienna","ror":"https://ror.org/03prydq77","country_code":"AT","type":"education","lineage":["https://openalex.org/I129774422"]},{"id":"https://openalex.org/I159176309","display_name":"Universit\u00e4t Hamburg","ror":"https://ror.org/00g30e956","country_code":"DE","type":"education","lineage":["https://openalex.org/I159176309"]},{"id":"https://openalex.org/I189712700","display_name":"University of Konstanz","ror":"https://ror.org/0546hnb39","country_code":"DE","type":"education","lineage":["https://openalex.org/I189712700"]},{"id":"https://openalex.org/I4210127348","display_name":"FORTH Institute of Electronic Structure and Laser","ror":"https://ror.org/02a3mhk13","country_code":"GR","type":"facility","lineage":["https://openalex.org/I4210127348","https://openalex.org/I8901234"]},{"id":"https://openalex.org/I4210160622","display_name":"Helsana Group (Switzerland)","ror":"https://ror.org/0530gr416","country_code":"CH","type":"company","lineage":["https://openalex.org/I4210160622"]},{"id":"https://openalex.org/I98358874","display_name":"Delft University of Technology","ror":"https://ror.org/02e2c7k09","country_code":"NL","type":"education","lineage":["https://openalex.org/I98358874"]}],"countries":["AT","CH","DE","GR","NL"],"is_corresponding":false,"raw_author_name":"Michael Kupper","raw_affiliation_strings":["FORTH, 70013, Heraklion, Greece","\\dagger Faculty of Mathematics, University of Vienna, 1090, Vienna, Austria","\\ddagger Department of Mathematics, University of Konstanz, 78464, Konstanz, Germany","\\P Delft Institute of Applied Mathematics, TU Delft, 2628 Delft, The Netherlands, and Institute of Applied and Computational Mathematics,","\\S Group Actuarial Department, Helvetia Insurance Group, 9001, St. Gallen, Switzerland","\\| Department of Mathematics, University of Hamburg, 20146, Hamburg, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"FORTH, 70013, Heraklion, Greece","institution_ids":["https://openalex.org/I4210127348"]},{"raw_affiliation_string":"\\dagger Faculty of Mathematics, University of Vienna, 1090, Vienna, Austria","institution_ids":["https://openalex.org/I129774422"]},{"raw_affiliation_string":"\\ddagger Department of Mathematics, University of Konstanz, 78464, Konstanz, Germany","institution_ids":["https://openalex.org/I189712700"]},{"raw_affiliation_string":"\\P Delft Institute of Applied Mathematics, TU Delft, 2628 Delft, The Netherlands, and Institute of Applied and Computational Mathematics,","institution_ids":["https://openalex.org/I98358874"]},{"raw_affiliation_string":"\\S Group Actuarial Department, Helvetia Insurance Group, 9001, St. Gallen, Switzerland","institution_ids":["https://openalex.org/I4210160622"]},{"raw_affiliation_string":"\\| Department of Mathematics, University of Hamburg, 20146, Hamburg, Germany","institution_ids":["https://openalex.org/I159176309"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5056727451","display_name":"Thibaut Lux","orcid":null},"institutions":[{"id":"https://openalex.org/I129774422","display_name":"University of Vienna","ror":"https://ror.org/03prydq77","country_code":"AT","type":"education","lineage":["https://openalex.org/I129774422"]},{"id":"https://openalex.org/I159176309","display_name":"Universit\u00e4t Hamburg","ror":"https://ror.org/00g30e956","country_code":"DE","type":"education","lineage":["https://openalex.org/I159176309"]},{"id":"https://openalex.org/I189712700","display_name":"University of Konstanz","ror":"https://ror.org/0546hnb39","country_code":"DE","type":"education","lineage":["https://openalex.org/I189712700"]},{"id":"https://openalex.org/I4210127348","display_name":"FORTH Institute of Electronic Structure and Laser","ror":"https://ror.org/02a3mhk13","country_code":"GR","type":"facility","lineage":["https://openalex.org/I4210127348","https://openalex.org/I8901234"]},{"id":"https://openalex.org/I4210160622","display_name":"Helsana Group (Switzerland)","ror":"https://ror.org/0530gr416","country_code":"CH","type":"company","lineage":["https://openalex.org/I4210160622"]},{"id":"https://openalex.org/I98358874","display_name":"Delft University of Technology","ror":"https://ror.org/02e2c7k09","country_code":"NL","type":"education","lineage":["https://openalex.org/I98358874"]}],"countries":["AT","CH","DE","GR","NL"],"is_corresponding":false,"raw_author_name":"Thibaut Lux","raw_affiliation_strings":["FORTH, 70013, Heraklion, Greece","\\dagger Faculty of Mathematics, University of Vienna, 1090, Vienna, Austria","\\S Group Actuarial Department, Helvetia Insurance Group, 9001, St. Gallen, Switzerland","\\ddagger Department of Mathematics, University of Konstanz, 78464, Konstanz, Germany","\\P Delft Institute of Applied Mathematics, TU Delft, 2628 Delft, The Netherlands, and Institute of Applied and Computational Mathematics,","\\| Department of Mathematics, University of Hamburg, 20146, Hamburg, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"FORTH, 70013, Heraklion, Greece","institution_ids":["https://openalex.org/I4210127348"]},{"raw_affiliation_string":"\\dagger Faculty of Mathematics, University of Vienna, 1090, Vienna, Austria","institution_ids":["https://openalex.org/I129774422"]},{"raw_affiliation_string":"\\S Group Actuarial Department, Helvetia Insurance Group, 9001, St. Gallen, Switzerland","institution_ids":["https://openalex.org/I4210160622"]},{"raw_affiliation_string":"\\ddagger Department of Mathematics, University of Konstanz, 78464, Konstanz, Germany","institution_ids":["https://openalex.org/I189712700"]},{"raw_affiliation_string":"\\P Delft Institute of Applied Mathematics, TU Delft, 2628 Delft, The Netherlands, and Institute of Applied and Computational Mathematics,","institution_ids":["https://openalex.org/I98358874"]},{"raw_affiliation_string":"\\| Department of Mathematics, University of Hamburg, 20146, Hamburg, Germany","institution_ids":["https://openalex.org/I159176309"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5067438441","display_name":"Antonis Papapantoleon","orcid":"https://orcid.org/0000-0002-9504-2822"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Antonis Papapantoleon","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5047214859","display_name":"Stephan Eckstein","orcid":"https://orcid.org/0000-0002-6407-2498"},"institutions":[{"id":"https://openalex.org/I129774422","display_name":"University of Vienna","ror":"https://ror.org/03prydq77","country_code":"AT","type":"education","lineage":["https://openalex.org/I129774422"]},{"id":"https://openalex.org/I159176309","display_name":"Universit\u00e4t Hamburg","ror":"https://ror.org/00g30e956","country_code":"DE","type":"education","lineage":["https://openalex.org/I159176309"]},{"id":"https://openalex.org/I189712700","display_name":"University of Konstanz","ror":"https://ror.org/0546hnb39","country_code":"DE","type":"education","lineage":["https://openalex.org/I189712700"]},{"id":"https://openalex.org/I4210127348","display_name":"FORTH Institute of Electronic Structure and Laser","ror":"https://ror.org/02a3mhk13","country_code":"GR","type":"facility","lineage":["https://openalex.org/I4210127348","https://openalex.org/I8901234"]},{"id":"https://openalex.org/I4210160622","display_name":"Helsana Group (Switzerland)","ror":"https://ror.org/0530gr416","country_code":"CH","type":"company","lineage":["https://openalex.org/I4210160622"]},{"id":"https://openalex.org/I98358874","display_name":"Delft University of Technology","ror":"https://ror.org/02e2c7k09","country_code":"NL","type":"education","lineage":["https://openalex.org/I98358874"]}],"countries":["AT","CH","DE","GR","NL"],"is_corresponding":false,"raw_author_name":"Stephan Eckstein","raw_affiliation_strings":["\\| Department of Mathematics, University of Hamburg, 20146, Hamburg, Germany","\\ddagger Department of Mathematics, University of Konstanz, 78464, Konstanz, Germany","\\P Delft Institute of Applied Mathematics, TU Delft, 2628 Delft, The Netherlands, and Institute of Applied and Computational Mathematics,","\\S Group Actuarial Department, Helvetia Insurance Group, 9001, St. Gallen, Switzerland","FORTH, 70013, Heraklion, Greece","\\dagger Faculty of Mathematics, University of Vienna, 1090, Vienna, Austria"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"\\| Department of Mathematics, University of Hamburg, 20146, Hamburg, Germany","institution_ids":["https://openalex.org/I159176309"]},{"raw_affiliation_string":"\\ddagger Department of Mathematics, University of Konstanz, 78464, Konstanz, Germany","institution_ids":["https://openalex.org/I189712700"]},{"raw_affiliation_string":"\\P Delft Institute of Applied Mathematics, TU Delft, 2628 Delft, The Netherlands, and Institute of Applied and Computational Mathematics,","institution_ids":["https://openalex.org/I98358874"]},{"raw_affiliation_string":"\\S Group Actuarial Department, Helvetia Insurance Group, 9001, St. Gallen, Switzerland","institution_ids":["https://openalex.org/I4210160622"]},{"raw_affiliation_string":"FORTH, 70013, Heraklion, Greece","institution_ids":["https://openalex.org/I4210127348"]},{"raw_affiliation_string":"\\dagger Faculty of Mathematics, University of Vienna, 1090, Vienna, Austria","institution_ids":["https://openalex.org/I129774422"]}]}],"institutions":[],"countries_distinct_count":5,"institutions_distinct_count":5,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.2985,"has_fulltext":false,"cited_by_count":10,"citation_normalized_percentile":{"value":0.8135818,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":96},"biblio":{"volume":"60","issue":"1","first_page":"410","last_page":"434"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10928","display_name":"Probabilistic and Robust Engineering Design","score":0.9980000257492065,"subfield":{"id":"https://openalex.org/subfields/1804","display_name":"Statistics, Probability and Uncertainty"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},"topics":[{"id":"https://openalex.org/T10928","display_name":"Probabilistic and Robust Engineering Design","score":0.9980000257492065,"subfield":{"id":"https://openalex.org/subfields/1804","display_name":"Statistics, Probability and Uncertainty"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T11413","display_name":"Risk and Portfolio Optimization","score":0.9864000082015991,"subfield":{"id":"https://openalex.org/subfields/1803","display_name":"Management Science and Operations Research"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T10067","display_name":"Stochastic processes and financial applications","score":0.9775000214576721,"subfield":{"id":"https://openalex.org/subfields/2003","display_name":"Finance"},"field":{"id":"https://openalex.org/fields/20","display_name":"Economics, Econometrics and Finance"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/duality","display_name":"Duality (order theory)","score":0.7614655494689941},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7169806957244873},{"id":"https://openalex.org/keywords/mathematical-economics","display_name":"Mathematical economics","score":0.4730968773365021},{"id":"https://openalex.org/keywords/subject","display_name":"Subject (documents)","score":0.44497764110565186},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3671843111515045},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.352999210357666},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3370370864868164},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.19435971975326538}],"concepts":[{"id":"https://openalex.org/C2778023678","wikidata":"https://www.wikidata.org/wiki/Q554403","display_name":"Duality (order theory)","level":2,"score":0.7614655494689941},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7169806957244873},{"id":"https://openalex.org/C144237770","wikidata":"https://www.wikidata.org/wiki/Q747534","display_name":"Mathematical economics","level":1,"score":0.4730968773365021},{"id":"https://openalex.org/C2777855551","wikidata":"https://www.wikidata.org/wiki/Q12310021","display_name":"Subject (documents)","level":2,"score":0.44497764110565186},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3671843111515045},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.352999210357666},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3370370864868164},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.19435971975326538},{"id":"https://openalex.org/C161191863","wikidata":"https://www.wikidata.org/wiki/Q199655","display_name":"Library science","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1137/21m144709x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/21m144709x","pdf_url":null,"source":{"id":"https://openalex.org/S897311980","display_name":"SIAM Journal on Control and Optimization","issn_l":"0363-0129","issn":["0363-0129","1095-7138"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Control and Optimization","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1709.00641","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1709.00641","pdf_url":"https://arxiv.org/pdf/1709.00641","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"text"},{"id":"pmh:oai:tudelft.nl:uuid:81625d08-2b0b-4b2e-8d59-f707fa16430a","is_oa":false,"landing_page_url":"http://resolver.tudelft.nl/uuid:81625d08-2b0b-4b2e-8d59-f707fa16430a","pdf_url":null,"source":{"id":"https://openalex.org/S4306400906","display_name":"Research Repository (Delft University of Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I98358874","host_organization_name":"Delft University of Technology","host_organization_lineage":["https://openalex.org/I98358874"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"journal article"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1709.00641","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1709.00641","pdf_url":"https://arxiv.org/pdf/1709.00641","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"text"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G4776667963","display_name":null,"funder_award_id":"HFRI-FM17-2152","funder_id":"https://openalex.org/F4320327859","funder_display_name":"Hellenic Foundation for Research and Innovation"},{"id":"https://openalex.org/G8521826871","display_name":"A transport view on stochastics and PDEs","funder_award_id":"P28661","funder_id":"https://openalex.org/F4320321181","funder_display_name":"Austrian Science Fund"},{"id":"https://openalex.org/G8988983655","display_name":"Macroprudential bank regulation: a continuous time approach","funder_award_id":"MA16-021","funder_id":"https://openalex.org/F4320321003","funder_display_name":"Vienna Science and Technology Fund"}],"funders":[{"id":"https://openalex.org/F4320321003","display_name":"Vienna Science and Technology Fund","ror":"https://ror.org/01f9mc681"},{"id":"https://openalex.org/F4320321181","display_name":"Austrian Science Fund","ror":"https://ror.org/013tf3c58"},{"id":"https://openalex.org/F4320327859","display_name":"Hellenic Foundation for Research and Innovation","ror":null}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":36,"referenced_works":["https://openalex.org/W55183739","https://openalex.org/W178872652","https://openalex.org/W1508957056","https://openalex.org/W1585160083","https://openalex.org/W1998972808","https://openalex.org/W2016649046","https://openalex.org/W2035481762","https://openalex.org/W2039411574","https://openalex.org/W2052956617","https://openalex.org/W2067696123","https://openalex.org/W2085737469","https://openalex.org/W2111246080","https://openalex.org/W2119436275","https://openalex.org/W2154140771","https://openalex.org/W2183160839","https://openalex.org/W2206379744","https://openalex.org/W2255104059","https://openalex.org/W2282761846","https://openalex.org/W2541828672","https://openalex.org/W2766949109","https://openalex.org/W2776620697","https://openalex.org/W2805509072","https://openalex.org/W2895859610","https://openalex.org/W2901082034","https://openalex.org/W2962717581","https://openalex.org/W2963905191","https://openalex.org/W3104641433","https://openalex.org/W3121841769","https://openalex.org/W3122101447","https://openalex.org/W3123641801","https://openalex.org/W3124960685","https://openalex.org/W3125070057","https://openalex.org/W3125152252","https://openalex.org/W3125316415","https://openalex.org/W3166939022","https://openalex.org/W4244967830"],"related_works":["https://openalex.org/W2748952813","https://openalex.org/W4388258507","https://openalex.org/W2392013855","https://openalex.org/W2357926602","https://openalex.org/W2374569605","https://openalex.org/W2386062718","https://openalex.org/W899618282","https://openalex.org/W2386129765","https://openalex.org/W2368742525","https://openalex.org/W2364803570"],"abstract_inverted_index":{"&lt;p&gt;Motivated":[0],"by":[1],"applications":[2],"in":[3,29,49,130,135,148,153,157,190],"model-free":[4],"finance":[5],"and":[6,64,96],"quantitative":[7],"risk":[8],"management,":[9],"we":[10],"consider":[11],"Frechet":[12,43,115],"classes":[13,44,129],"of":[14,68,94,102,133,151],"multivariate":[15],"distribution":[16,24],"functions":[17],"where":[18,88],"additional":[19],"information":[20],"on":[21,57,166],"the":[22,30,50,65,69,74,83,120,131,136,149,154,167],"joint":[23],"is":[25,32,90],"assumed,":[26],"while":[27,138],"uncertainty":[28,134,152],"marginals":[31],"also":[33],"possible.":[34],"We":[35,71,117],"derive":[36],"optimal":[37],"transport":[38,76],"duality":[39],"results":[40,48,59],"for":[41,60,82,113,127],"these":[42,114,128,186],"that":[45,73,119,142],"extend":[46],"previous":[47],"related":[51],"literature.":[52],"These":[53],"proofs":[54],"are":[55,124,144,188],"based":[56],"representation":[58],"convex":[61],"increasing":[62],"functionals":[63],"explicit":[66,80],"computation":[67],"conjugates.":[70],"show":[72,118],"dual":[75],"problem":[77],"admits":[78],"an":[79,98],"solution":[81],"function":[84],"f":[85],"=":[86],"1B,":[87],"B":[89],"a":[91,139],"rectangular":[92],"subset":[93],"Rd,":[95],"provide":[97,109],"intuitive":[99],"geometric":[100],"interpretation":[101],"this":[103],"result.":[104],"The":[105,160],"improved":[106,121,168],"Frechet-Hoeffding":[107,122,169],"bounds":[108,112,123,187],"ad":[110],"hoc":[111],"classes.":[116],"pointwise":[125,146],"sharp":[126,147,189],"presence":[132],"marginals,":[137,155],"counterexample":[140],"yields":[141],"they":[143],"not":[145],"absence":[150],"even":[156],"dimension":[158,191],"2.":[159],"latter":[161],"result":[162],"sheds":[163],"new":[164],"light":[165],"bounds,":[170],"since":[171],"Tankov":[172],"[J.":[173],"Appl.":[174],"Probab.,":[175],"48":[176],"(2011),":[177],"pp.":[178],"389-403]":[179],"has":[180],"showed":[181],"that,":[182],"under":[183],"certain":[184],"conditions,":[185],"2.&lt;/p&gt;":[192]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":2},{"year":2016,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2022-10-01T00:00:00"}
