{"id":"https://openalex.org/W2008570142","doi":"https://doi.org/10.1214/009117907000000222","title":"Max-Plus decomposition of supermartingales and convex order. Application to American options and portfolio insurance","display_name":"Max-Plus decomposition of supermartingales and convex order. Application to American options and portfolio insurance","publication_year":2008,"publication_date":"2008-03-01","ids":{"openalex":"https://openalex.org/W2008570142","doi":"https://doi.org/10.1214/009117907000000222","mag":"2008570142"},"language":"en","primary_location":{"id":"doi:10.1214/009117907000000222","doi":"https://doi.org/10.1214/009117907000000222","is_oa":true,"landing_page_url":"https://doi.org/10.1214/009117907000000222","pdf_url":"https://projecteuclid.org/journals/annals-of-probability/volume-36/issue-2/Max-Plus-decomposition-of-supermartingales-and-convex-order-Application-to/10.1214/009117907000000222.pdf","source":{"id":"https://openalex.org/S40212770","display_name":"The Annals of Probability","issn_l":"0091-1798","issn":["0091-1798","2168-894X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["abdc-a-star","anvur-class-a","anvur-scientific","cwts-core","dongbi-a","jufo-3","norway-2","poland-140","russia-white-list-1"],"host_organization":"https://openalex.org/P4310319881","host_organization_name":"Institute of Mathematical Statistics","host_organization_lineage":["https://openalex.org/P4310319881"],"host_organization_lineage_names":["Institute of Mathematical Statistics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Annals of Probability","raw_type":"journal-article"},"volume":null,"type":"article","is_traditional":true,"indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://projecteuclid.org/journals/annals-of-probability/volume-36/issue-2/Max-Plus-decomposition-of-supermartingales-and-convex-order-Application-to/10.1214/009117907000000222.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5112311167","display_name":"Nicole El Karoui","orcid":"https://orcid.org/0000-0002-0822-9198","observed_orcids":["https://orcid.org/0000-0002-0822-9198"]},"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"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Nicole El Karoui","raw_affiliation_strings":["Ecole Polytechnique"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Ecole Polytechnique","institution_ids":["https://openalex.org/I142476485"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5041368824","display_name":"Asma Meziou","orcid":null,"observed_orcids":[]},"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"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Asma Meziou","raw_affiliation_strings":["Ecole Polytechnique"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Ecole Polytechnique","institution_ids":["https://openalex.org/I142476485"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I142476485"],"apc_list":null,"apc_paid":null,"fwci":2.5688,"has_fulltext":true,"cited_by_count":17,"citation_normalized_percentile":{"value":0.91748742,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":87,"max":97},"biblio":{"volume":"36","issue":"2","first_page":"647","last_page":"697"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10067","display_name":"Stochastic processes and financial applications","score":0.9994999766349792,"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":0.9994999766349792,"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/T11720","display_name":"Probability and Risk Models","score":0.00019999999494757503,"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/T11413","display_name":"Risk and Portfolio Optimization","score":9.999999747378752e-05,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/max-plus-algebra","display_name":"max-plus algebra","score":0.9279999732971191},{"id":"https://openalex.org/keywords/convex-order","display_name":"convex order","score":0.7260000109672546},{"id":"https://openalex.org/keywords/american-options","display_name":"American options","score":0.9150000214576721},{"id":"https://openalex.org/keywords/optimal-stopping","display_name":"optimal stopping","score":0.9539999961853027},{"id":"https://openalex.org/keywords/portfolio-insurance","display_name":"portfolio insurance","score":0.9229999780654907},{"id":"https://openalex.org/keywords/diffusion","display_name":"diffusion","score":0.7549999952316284}],"concepts":[{"id":"https://openalex.org/C48406656","wikidata":"https://www.wikidata.org/wiki/Q534112","display_name":"Martingale (probability theory)","level":2,"score":0.7320120930671692},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7298818826675415},{"id":"https://openalex.org/C95611797","wikidata":"https://www.wikidata.org/wiki/Q17502105","display_name":"Infimum and supremum","level":2,"score":0.7127901315689087},{"id":"https://openalex.org/C58435881","wikidata":"https://www.wikidata.org/wiki/Q1868500","display_name":"Local martingale","level":3,"score":0.6113377809524536},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.6002464890480042},{"id":"https://openalex.org/C52832964","wikidata":"https://www.wikidata.org/wiki/Q2027347","display_name":"Optional stopping theorem","level":3,"score":0.5049815773963928},{"id":"https://openalex.org/C144237770","wikidata":"https://www.wikidata.org/wiki/Q747534","display_name":"Mathematical economics","level":1,"score":0.4812731146812439},{"id":"https://openalex.org/C2780821815","wikidata":"https://www.wikidata.org/wiki/Q5340806","display_name":"Portfolio","level":2,"score":0.46984854340553284},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.46481117606163025},{"id":"https://openalex.org/C99414536","wikidata":"https://www.wikidata.org/wiki/Q7098950","display_name":"Optimal stopping","level":2,"score":0.448047012090683},{"id":"https://openalex.org/C124681953","wikidata":"https://www.wikidata.org/wiki/Q339062","display_name":"Decomposition","level":2,"score":0.4339030086994171},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.4133971333503723},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.37076589465141296},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.2396901547908783},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.1387287676334381},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.12478700280189514},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0}],"mesh":[],"locations_count":7,"locations":[{"id":"doi:10.1214/009117907000000222","doi":"https://doi.org/10.1214/009117907000000222","is_oa":true,"landing_page_url":"https://doi.org/10.1214/009117907000000222","pdf_url":"https://projecteuclid.org/journals/annals-of-probability/volume-36/issue-2/Max-Plus-decomposition-of-supermartingales-and-convex-order-Application-to/10.1214/009117907000000222.pdf","source":{"id":"https://openalex.org/S40212770","display_name":"The Annals of Probability","issn_l":"0091-1798","issn":["0091-1798","2168-894X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["abdc-a-star","anvur-class-a","anvur-scientific","cwts-core","dongbi-a","jufo-3","norway-2","poland-140","russia-white-list-1"],"host_organization":"https://openalex.org/P4310319881","host_organization_name":"Institute of Mathematical Statistics","host_organization_lineage":["https://openalex.org/P4310319881"],"host_organization_lineage_names":["Institute of Mathematical Statistics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Annals of Probability","raw_type":"journal-article"},{"id":"pmh:oai:RePEc:arx:papers:0804.2561","doi":null,"is_oa":false,"landing_page_url":"http://arxiv.org/pdf/0804.2561","pdf_url":"http://arxiv.org/pdf/0804.2561","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,"listed_in":[],"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":"preprint"},{"id":"pmh:oai:arXiv.org:0804.2561","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/0804.2561","pdf_url":"https://arxiv.org/pdf/0804.2561","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":null,"raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.312.8810","doi":null,"is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.312.8810","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://arxiv.org/pdf/0804.2561v1.pdf","raw_type":"text"},{"id":"pmh:oai:CULeuclid:euclid.aop/1204306963","doi":null,"is_oa":false,"landing_page_url":"https://projecteuclid.org/euclid.aop/1204306963","pdf_url":null,"source":{"id":"https://openalex.org/S4306400787","display_name":"Project Euclid (Cornell University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"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:HAL:hal-00708488v1","doi":null,"is_oa":false,"landing_page_url":"https://hal.science/hal-00708488","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I4405252976","host_organization_name":"Centre pour la Communication Scientifique Directe","host_organization_lineage":["https://openalex.org/I4405252976"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"The Annals of Probability, 2008, 36 (2), pp.647-697","raw_type":"info:eu-repo/semantics/article"},{"id":"doi:10.48550/arxiv.0804.2561","doi":"https://doi.org/10.48550/arxiv.0804.2561","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.0804.2561","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article-journal"}],"best_oa_location":{"id":"doi:10.1214/009117907000000222","doi":"https://doi.org/10.1214/009117907000000222","is_oa":true,"landing_page_url":"https://doi.org/10.1214/009117907000000222","pdf_url":"https://projecteuclid.org/journals/annals-of-probability/volume-36/issue-2/Max-Plus-decomposition-of-supermartingales-and-convex-order-Application-to/10.1214/009117907000000222.pdf","source":{"id":"https://openalex.org/S40212770","display_name":"The Annals of Probability","issn_l":"0091-1798","issn":["0091-1798","2168-894X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["abdc-a-star","anvur-class-a","anvur-scientific","cwts-core","dongbi-a","jufo-3","norway-2","poland-140","russia-white-list-1"],"host_organization":"https://openalex.org/P4310319881","host_organization_name":"Institute of Mathematical Statistics","host_organization_lineage":["https://openalex.org/P4310319881"],"host_organization_lineage_names":["Institute of Mathematical Statistics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Annals of Probability","raw_type":"journal-article"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2008570142.pdf","grobid_xml":"https://content.openalex.org/works/W2008570142.grobid-xml"},"referenced_works_count":46,"referenced_works":["https://openalex.org/W20588324","https://openalex.org/W116070899","https://openalex.org/W125726264","https://openalex.org/W166250193","https://openalex.org/W180678876","https://openalex.org/W187591943","https://openalex.org/W204533568","https://openalex.org/W1509668884","https://openalex.org/W1524118122","https://openalex.org/W1526512085","https://openalex.org/W1569544946","https://openalex.org/W1580561995","https://openalex.org/W1594270709","https://openalex.org/W1660435996","https://openalex.org/W1768768251","https://openalex.org/W1920130955","https://openalex.org/W1978300329","https://openalex.org/W1979547553","https://openalex.org/W1984328418","https://openalex.org/W1991466857","https://openalex.org/W1995118028","https://openalex.org/W2000827368","https://openalex.org/W2015228311","https://openalex.org/W2015609726","https://openalex.org/W2017141753","https://openalex.org/W2018055712","https://openalex.org/W2042775870","https://openalex.org/W2046623907","https://openalex.org/W2057110927","https://openalex.org/W2067286730","https://openalex.org/W2073131960","https://openalex.org/W2083505075","https://openalex.org/W2090069585","https://openalex.org/W2090789457","https://openalex.org/W2098384778","https://openalex.org/W2123893652","https://openalex.org/W2129462326","https://openalex.org/W2144846366","https://openalex.org/W2171361952","https://openalex.org/W2333470148","https://openalex.org/W2796337403","https://openalex.org/W4229911014","https://openalex.org/W4236811028","https://openalex.org/W4236866385","https://openalex.org/W4285719527","https://openalex.org/W6603017738"],"related_works":["https://openalex.org/W1776630886","https://openalex.org/W2046623907","https://openalex.org/W4288640509","https://openalex.org/W6941265331","https://openalex.org/W2002265316","https://openalex.org/W2809069650","https://openalex.org/W2596835554","https://openalex.org/W2288542183","https://openalex.org/W2904540600","https://openalex.org/W2333820754"],"abstract_inverted_index":{"We":[0],"are":[1,68],"concerned":[2],"with":[3],"a":[4,25,101],"new":[5],"type":[6],"of":[7,21,28],"supermartingale":[8,20,41],"decomposition":[9,42],"in":[10,17,44,86],"the":[11,39,48,57,75,81,87,97,110],"Max-Plus":[12,40],"algebra,":[13],"which":[14],"essentially":[15],"consists":[16],"expressing":[18],"any":[19],"class":[22],"$(\\mathcal{D})$":[23],"as":[24],"conditional":[26],"expectation":[27],"some":[29],"running":[30],"supremum":[31],"process.":[32],"As":[33],"an":[34,89],"application,":[35],"we":[36,84],"show":[37],"how":[38],"allows,":[43],"particular,":[45],"to":[46,55,95],"solve":[47,85],"American":[49],"optimal":[50],"stopping":[51],"problem":[52,91],"without":[53],"having":[54],"compute":[56],"option":[58],"price.":[59],"Some":[60],"illustrative":[61],"examples":[62],"based":[63,79],"on":[64,80,113],"one-dimensional":[65],"diffusion":[66],"processes":[67],"then":[69],"provided.":[70],"Another":[71],"interesting":[72],"application":[73],"concerns":[74],"portfolio":[76],"insurance.":[77],"Hence,":[78],"\u201cMax-Plus":[82],"martingale,\u201d":[83],"paper":[88],"optimization":[90],"whose":[92],"aim":[93],"is":[94],"find":[96],"best":[98],"martingale":[99],"dominating":[100],"given":[102],"floor":[103],"process":[104],"(on":[105],"every":[106],"intermediate":[107],"date),":[108],"w.r.t.":[109],"convex":[111],"order":[112],"terminal":[114],"values.":[115]},"counts_by_year":[{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":2},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":1},{"year":2012,"cited_by_count":3}],"updated_date":"2026-11-04T10:54:05.112534","created_date":"2025-10-10T00:00:00"}