{"id":"https://openalex.org/W2339312800","doi":"https://doi.org/10.1007/s00780-016-0299-x","title":"An explicit martingale version of the one-dimensional Brenier theorem","display_name":"An explicit martingale version of the one-dimensional Brenier theorem","publication_year":2016,"publication_date":"2016-04-18","ids":{"openalex":"https://openalex.org/W2339312800","doi":"https://doi.org/10.1007/s00780-016-0299-x","mag":"2339312800"},"language":"en","primary_location":{"id":"doi:10.1007/s00780-016-0299-x","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s00780-016-0299-x","pdf_url":null,"source":{"id":"https://openalex.org/S172526255","display_name":"Finance and Stochastics","issn_l":"0949-2984","issn":["0949-2984","1432-1122"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Finance and Stochastics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5069915038","display_name":"Pierre Henry\u2010Labord\u00e8re","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Pierre Henry-Labord\u00e8re","raw_affiliation_strings":["Global Markets Quantitative Research, Soci\u00e9t\u00e9 G\u00e9n\u00e9rale, 17 cours Valmy, La D\u00e9fense, Paris, France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Global Markets Quantitative Research, Soci\u00e9t\u00e9 G\u00e9n\u00e9rale, 17 cours Valmy, La D\u00e9fense, Paris, France","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5105990961","display_name":"Nizar Touzi","orcid":null},"institutions":[{"id":"https://openalex.org/I142476485","display_name":"\u00c9cole Polytechnique","ror":"https://ror.org/05hy3tk52","country_code":"FR","type":"education","lineage":["https://openalex.org/I142476485","https://openalex.org/I4210145102"]},{"id":"https://openalex.org/I4210107641","display_name":"Centre de Math\u00e9matiques Appliqu\u00e9es","ror":"https://ror.org/012e1xn46","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I1326498283","https://openalex.org/I142476485","https://openalex.org/I4210107641","https://openalex.org/I4210141950","https://openalex.org/I4210145102"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Nizar Touzi","raw_affiliation_strings":["Centre de Math\u00e9matiques Appliqu\u00e9es, Ecole Polytechnique Paris, Paris, France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Centre de Math\u00e9matiques Appliqu\u00e9es, Ecole Polytechnique Paris, Paris, France","institution_ids":["https://openalex.org/I4210107641","https://openalex.org/I142476485"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5069915038"],"corresponding_institution_ids":[],"apc_list":{"value":2290,"currency":"EUR","value_usd":2890},"apc_paid":null,"fwci":16.4626,"has_fulltext":false,"cited_by_count":75,"citation_normalized_percentile":{"value":0.99136235,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":96,"max":99},"biblio":{"volume":"20","issue":"3","first_page":"635","last_page":"668"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10067","display_name":"Stochastic processes and financial applications","score":0.9995999932289124,"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"}},"topics":[{"id":"https://openalex.org/T10067","display_name":"Stochastic processes and financial applications","score":0.9995999932289124,"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"}},{"id":"https://openalex.org/T12011","display_name":"Insurance, Mortality, Demography, Risk Management","score":0.9857000112533569,"subfield":{"id":"https://openalex.org/subfields/3317","display_name":"Demography"},"field":{"id":"https://openalex.org/fields/33","display_name":"Social Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T12137","display_name":"Economic theories and models","score":0.9846000075340271,"subfield":{"id":"https://openalex.org/subfields/2002","display_name":"Economics and Econometrics"},"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/martingale","display_name":"Martingale (probability theory)","score":0.8623918294906616},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7839813232421875},{"id":"https://openalex.org/keywords/mathematical-finance","display_name":"Mathematical finance","score":0.7360731959342957},{"id":"https://openalex.org/keywords/local-martingale","display_name":"Local martingale","score":0.5566394329071045},{"id":"https://openalex.org/keywords/monotone-polygon","display_name":"Monotone polygon","score":0.5519471168518066},{"id":"https://openalex.org/keywords/mathematical-economics","display_name":"Mathematical economics","score":0.481076717376709},{"id":"https://openalex.org/keywords/monotonic-function","display_name":"Monotonic function","score":0.4391278624534607},{"id":"https://openalex.org/keywords/complement","display_name":"Complement (music)","score":0.42173928022384644},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3904974162578583},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.37575390934944153},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3302108645439148},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.21287578344345093},{"id":"https://openalex.org/keywords/finance","display_name":"Finance","score":0.14121156930923462},{"id":"https://openalex.org/keywords/economics","display_name":"Economics","score":0.0948638916015625},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.08826351165771484}],"concepts":[{"id":"https://openalex.org/C48406656","wikidata":"https://www.wikidata.org/wiki/Q534112","display_name":"Martingale (probability theory)","level":2,"score":0.8623918294906616},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7839813232421875},{"id":"https://openalex.org/C93373587","wikidata":"https://www.wikidata.org/wiki/Q335632","display_name":"Mathematical finance","level":2,"score":0.7360731959342957},{"id":"https://openalex.org/C58435881","wikidata":"https://www.wikidata.org/wiki/Q1868500","display_name":"Local martingale","level":3,"score":0.5566394329071045},{"id":"https://openalex.org/C2834757","wikidata":"https://www.wikidata.org/wiki/Q4925424","display_name":"Monotone polygon","level":2,"score":0.5519471168518066},{"id":"https://openalex.org/C144237770","wikidata":"https://www.wikidata.org/wiki/Q747534","display_name":"Mathematical economics","level":1,"score":0.481076717376709},{"id":"https://openalex.org/C72169020","wikidata":"https://www.wikidata.org/wiki/Q194404","display_name":"Monotonic function","level":2,"score":0.4391278624534607},{"id":"https://openalex.org/C112313634","wikidata":"https://www.wikidata.org/wiki/Q7886648","display_name":"Complement (music)","level":5,"score":0.42173928022384644},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3904974162578583},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.37575390934944153},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3302108645439148},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.21287578344345093},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.14121156930923462},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0948638916015625},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.08826351165771484},{"id":"https://openalex.org/C188082640","wikidata":"https://www.wikidata.org/wiki/Q1780899","display_name":"Complementation","level":4,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C127716648","wikidata":"https://www.wikidata.org/wiki/Q104053","display_name":"Phenotype","level":3,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1007/s00780-016-0299-x","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s00780-016-0299-x","pdf_url":null,"source":{"id":"https://openalex.org/S172526255","display_name":"Finance and Stochastics","issn_l":"0949-2984","issn":["0949-2984","1432-1122"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Finance and Stochastics","raw_type":"journal-article"},{"id":"pmh:oai:HAL:hal-04573426v1","is_oa":false,"landing_page_url":"https://hal.science/hal-04573426","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Finance and Stochastics, 2016, 20 (3), pp.635-668. ⟨10.1007/s00780-016-0299-x⟩","raw_type":"Journal articles"},{"id":"pmh:oai:RePEc:spr:finsto:v:20:y:2016:i:3:d:10.1007_s00780-016-0299-x","is_oa":false,"landing_page_url":"http://link.springer.com/10.1007/s00780-016-0299-x","pdf_url":null,"source":{"id":"https://openalex.org/S4306401271","display_name":"RePEc: Research Papers in Economics","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I77793887","host_organization_name":"Federal Reserve Bank of St. Louis","host_organization_lineage":["https://openalex.org/I77793887"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/8","score":0.44999998807907104,"display_name":"Decent work and economic growth"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":54,"referenced_works":["https://openalex.org/W583356579","https://openalex.org/W599484449","https://openalex.org/W1533719226","https://openalex.org/W1585160083","https://openalex.org/W1589034765","https://openalex.org/W1768680319","https://openalex.org/W1842249978","https://openalex.org/W1978210787","https://openalex.org/W1978744255","https://openalex.org/W1982317099","https://openalex.org/W1986392102","https://openalex.org/W1989924369","https://openalex.org/W1997543744","https://openalex.org/W2046080453","https://openalex.org/W2048594534","https://openalex.org/W2070589948","https://openalex.org/W2072927167","https://openalex.org/W2087001647","https://openalex.org/W2101285166","https://openalex.org/W2106141948","https://openalex.org/W2106198462","https://openalex.org/W2111246080","https://openalex.org/W2115438349","https://openalex.org/W2129216683","https://openalex.org/W2130918614","https://openalex.org/W2135234300","https://openalex.org/W2143118268","https://openalex.org/W2152245377","https://openalex.org/W2153166227","https://openalex.org/W2156859052","https://openalex.org/W2169203802","https://openalex.org/W2183160839","https://openalex.org/W2283275366","https://openalex.org/W2323026722","https://openalex.org/W2330922995","https://openalex.org/W2601855024","https://openalex.org/W2791633628","https://openalex.org/W2913240118","https://openalex.org/W2962709856","https://openalex.org/W3098180202","https://openalex.org/W3100234850","https://openalex.org/W3100939514","https://openalex.org/W3103030658","https://openalex.org/W3105471026","https://openalex.org/W3121720857","https://openalex.org/W3122203059","https://openalex.org/W3123229189","https://openalex.org/W3123655054","https://openalex.org/W3124843848","https://openalex.org/W3124960685","https://openalex.org/W3125330115","https://openalex.org/W3125589302","https://openalex.org/W4285719527","https://openalex.org/W4290688657"],"related_works":["https://openalex.org/W1489292980","https://openalex.org/W2795079910","https://openalex.org/W2951610245","https://openalex.org/W4289784528","https://openalex.org/W2509733388","https://openalex.org/W1430963189","https://openalex.org/W2021764764","https://openalex.org/W2013937202","https://openalex.org/W1973175113","https://openalex.org/W2138588791"],"abstract_inverted_index":null,"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":5},{"year":2024,"cited_by_count":4},{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":9},{"year":2021,"cited_by_count":9},{"year":2020,"cited_by_count":5},{"year":2019,"cited_by_count":13},{"year":2018,"cited_by_count":7},{"year":2017,"cited_by_count":9},{"year":2016,"cited_by_count":6},{"year":2015,"cited_by_count":3}],"updated_date":"2026-05-07T13:39:58.223016","created_date":"2025-10-10T00:00:00"}