{"id":"https://openalex.org/W3089667743","doi":"https://doi.org/10.1051/ro/2016026","title":"Multivariate stochastic dominance for risk averters and risk seekers","display_name":"Multivariate stochastic dominance for risk averters and risk seekers","publication_year":2016,"publication_date":"2016-03-31","ids":{"openalex":"https://openalex.org/W3089667743","doi":"https://doi.org/10.1051/ro/2016026","mag":"3089667743"},"language":"en","primary_location":{"id":"doi:10.1051/ro/2016026","is_oa":false,"landing_page_url":"https://doi.org/10.1051/ro/2016026","pdf_url":null,"source":{"id":"https://openalex.org/S20631277","display_name":"RAIRO - Operations Research","issn_l":"0399-0559","issn":["0399-0559","1290-3868"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319748","host_organization_name":"EDP Sciences","host_organization_lineage":["https://openalex.org/P4310319748"],"host_organization_lineage_names":["EDP Sciences"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"RAIRO - Operations Research","raw_type":"journal-article"},"type":"preprint","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://www.numdam.org/item/10.1051/ro/2016026.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5101666020","display_name":"Xu Guo","orcid":"https://orcid.org/0000-0003-4037-8633"},"institutions":[{"id":"https://openalex.org/I25254941","display_name":"Beijing Normal University","ror":"https://ror.org/022k4wk35","country_code":"CN","type":"education","lineage":["https://openalex.org/I25254941"]},{"id":"https://openalex.org/I9842412","display_name":"Nanjing University of Aeronautics and Astronautics","ror":"https://ror.org/01scyh794","country_code":"CN","type":"education","lineage":["https://openalex.org/I9842412"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xu Guo","raw_affiliation_strings":["College of Economics and Management, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, P.R. China","School of Statistics, Beijing Normal University, Beijing, P.R. China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"College of Economics and Management, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, P.R. China","institution_ids":["https://openalex.org/I9842412"]},{"raw_affiliation_string":"School of Statistics, Beijing Normal University, Beijing, P.R. China","institution_ids":["https://openalex.org/I25254941"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5045661677","display_name":"Wing\u2010Keung Wong","orcid":"https://orcid.org/0000-0001-6755-572X"},"institutions":[{"id":"https://openalex.org/I141568987","display_name":"Hong Kong Baptist University","ror":"https://ror.org/0145fw131","country_code":"HK","type":"education","lineage":["https://openalex.org/I141568987"]},{"id":"https://openalex.org/I143578492","display_name":"Asia University","ror":"https://ror.org/038a1tp19","country_code":"TW","type":"education","lineage":["https://openalex.org/I143578492"]},{"id":"https://openalex.org/I165488957","display_name":"Lingnan University","ror":"https://ror.org/0563pg902","country_code":"HK","type":"education","lineage":["https://openalex.org/I165488957"]}],"countries":["HK","TW"],"is_corresponding":false,"raw_author_name":"Wing-Keung Wong","raw_affiliation_strings":["Department of Economics, Lingnan University, Hong Kong, P.R. China","Department of Finance, Asia University, Taiwan","Faculty of Economics, Hong Kong Baptist University, Hong Kong, P.R. China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Economics, Lingnan University, Hong Kong, P.R. China","institution_ids":["https://openalex.org/I165488957"]},{"raw_affiliation_string":"Department of Finance, Asia University, Taiwan","institution_ids":["https://openalex.org/I143578492"]},{"raw_affiliation_string":"Faculty of Economics, Hong Kong Baptist University, Hong Kong, P.R. China","institution_ids":["https://openalex.org/I141568987"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":3.3558,"has_fulltext":true,"cited_by_count":21,"citation_normalized_percentile":{"value":0.9238948,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"50","issue":"3","first_page":"575","last_page":"586"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10315","display_name":"Decision-Making and Behavioral Economics","score":0.9650999903678894,"subfield":{"id":"https://openalex.org/subfields/1800","display_name":"General Decision Sciences"},"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/T10315","display_name":"Decision-Making and Behavioral Economics","score":0.9650999903678894,"subfield":{"id":"https://openalex.org/subfields/1800","display_name":"General Decision Sciences"},"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/T10050","display_name":"Multi-Criteria Decision Making","score":0.9571999907493591,"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/T11871","display_name":"Advanced Statistical Methods and Models","score":0.941100001335144,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/stochastic-dominance","display_name":"Stochastic dominance","score":0.8632823824882507},{"id":"https://openalex.org/keywords/seekers","display_name":"Seekers","score":0.6853391528129578},{"id":"https://openalex.org/keywords/multivariate-statistics","display_name":"Multivariate statistics","score":0.6806643009185791},{"id":"https://openalex.org/keywords/univariate","display_name":"Univariate","score":0.573660671710968},{"id":"https://openalex.org/keywords/diversification","display_name":"Diversification (marketing strategy)","score":0.5405731201171875},{"id":"https://openalex.org/keywords/econometrics","display_name":"Econometrics","score":0.4849672317504883},{"id":"https://openalex.org/keywords/separable-space","display_name":"Separable space","score":0.4303137958049774},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.40227174758911133},{"id":"https://openalex.org/keywords/actuarial-science","display_name":"Actuarial science","score":0.384404718875885},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.34843987226486206},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.28159618377685547},{"id":"https://openalex.org/keywords/economics","display_name":"Economics","score":0.28004246950149536},{"id":"https://openalex.org/keywords/business","display_name":"Business","score":0.1327340006828308},{"id":"https://openalex.org/keywords/marketing","display_name":"Marketing","score":0.0918043851852417},{"id":"https://openalex.org/keywords/political-science","display_name":"Political science","score":0.0756402313709259}],"concepts":[{"id":"https://openalex.org/C33252445","wikidata":"https://www.wikidata.org/wiki/Q3713315","display_name":"Stochastic dominance","level":2,"score":0.8632823824882507},{"id":"https://openalex.org/C2776493517","wikidata":"https://www.wikidata.org/wiki/Q1479542","display_name":"Seekers","level":2,"score":0.6853391528129578},{"id":"https://openalex.org/C161584116","wikidata":"https://www.wikidata.org/wiki/Q1952580","display_name":"Multivariate statistics","level":2,"score":0.6806643009185791},{"id":"https://openalex.org/C199163554","wikidata":"https://www.wikidata.org/wiki/Q1681619","display_name":"Univariate","level":3,"score":0.573660671710968},{"id":"https://openalex.org/C180916674","wikidata":"https://www.wikidata.org/wiki/Q3711935","display_name":"Diversification (marketing strategy)","level":2,"score":0.5405731201171875},{"id":"https://openalex.org/C149782125","wikidata":"https://www.wikidata.org/wiki/Q160039","display_name":"Econometrics","level":1,"score":0.4849672317504883},{"id":"https://openalex.org/C70710897","wikidata":"https://www.wikidata.org/wiki/Q680081","display_name":"Separable space","level":2,"score":0.4303137958049774},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.40227174758911133},{"id":"https://openalex.org/C162118730","wikidata":"https://www.wikidata.org/wiki/Q1128453","display_name":"Actuarial science","level":1,"score":0.384404718875885},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.34843987226486206},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.28159618377685547},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.28004246950149536},{"id":"https://openalex.org/C144133560","wikidata":"https://www.wikidata.org/wiki/Q4830453","display_name":"Business","level":0,"score":0.1327340006828308},{"id":"https://openalex.org/C162853370","wikidata":"https://www.wikidata.org/wiki/Q39809","display_name":"Marketing","level":1,"score":0.0918043851852417},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0756402313709259},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0}],"mesh":[],"locations_count":6,"locations":[{"id":"doi:10.1051/ro/2016026","is_oa":false,"landing_page_url":"https://doi.org/10.1051/ro/2016026","pdf_url":null,"source":{"id":"https://openalex.org/S20631277","display_name":"RAIRO - Operations Research","issn_l":"0399-0559","issn":["0399-0559","1290-3868"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319748","host_organization_name":"EDP Sciences","host_organization_lineage":["https://openalex.org/P4310319748"],"host_organization_lineage_names":["EDP Sciences"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"RAIRO - Operations Research","raw_type":"journal-article"},{"id":"pmh:oai::70637","is_oa":false,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4306400553","display_name":"Munich Personal RePEc Archive (Ludwig Maximilian University of Munich)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I8204097","host_organization_name":"Ludwig-Maximilians-Universit\u00e4t M\u00fcnchen","host_organization_lineage":["https://openalex.org/I8204097"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":"","raw_type":"MPRA Paper"},{"id":"pmh:oai:numdam.org:RO_2016__50_3_575_0","is_oa":true,"landing_page_url":"http://www.numdam.org/articles/10.1051/ro/2016026/","pdf_url":"https://www.numdam.org/item/10.1051/ro/2016026.pdf","source":{"id":"https://openalex.org/S4306402264","display_name":"French digital mathematics library (Numdam)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I70900168","host_organization_name":"Universit\u00e9 Savoie Mont Blanc","host_organization_lineage":["https://openalex.org/I70900168"],"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:commons.ln.edu.hk:sw_master-6449","is_oa":false,"landing_page_url":"https://commons.ln.edu.hk/sw_master/5449","pdf_url":null,"source":{"id":"https://openalex.org/S4377196536","display_name":"Digital Commons - Lingnan (Lingnan University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I165488957","host_organization_name":"Lingnan University","host_organization_lineage":["https://openalex.org/I165488957"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Staff Publications","raw_type":"text"},{"id":"mag:3089667743","is_oa":false,"landing_page_url":"https://econpapers.repec.org/RePEc:pra:mprapa:70637","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":"RePEc: Research Papers in Economics","raw_type":null},{"id":"mag:3148528286","is_oa":false,"landing_page_url":"https://ideas.repec.org/p/pra/mprapa/70637.html","pdf_url":null,"source":{"id":"https://openalex.org/S4306520297","display_name":"MPRA Paper","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"MPRA Paper","raw_type":null}],"best_oa_location":{"id":"pmh:oai:numdam.org:RO_2016__50_3_575_0","is_oa":true,"landing_page_url":"http://www.numdam.org/articles/10.1051/ro/2016026/","pdf_url":"https://www.numdam.org/item/10.1051/ro/2016026.pdf","source":{"id":"https://openalex.org/S4306402264","display_name":"French digital mathematics library (Numdam)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I70900168","host_organization_name":"Universit\u00e9 Savoie Mont Blanc","host_organization_lineage":["https://openalex.org/I70900168"],"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"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G7548687035","display_name":null,"funder_award_id":"BK20150732","funder_id":"https://openalex.org/F4320322769","funder_display_name":"Natural Science Foundation of Jiangsu Province"}],"funders":[{"id":"https://openalex.org/F4320320955","display_name":"Hong Kong Baptist University","ror":"https://ror.org/0145fw131"},{"id":"https://openalex.org/F4320321529","display_name":"Chiang Mai University","ror":"https://ror.org/05m2fqn25"},{"id":"https://openalex.org/F4320321605","display_name":"Government of Jiangsu Province","ror":"https://ror.org/004svx814"},{"id":"https://openalex.org/F4320322769","display_name":"Natural Science Foundation of Jiangsu Province","ror":"https://ror.org/01h0zpd94"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3089667743.pdf","grobid_xml":"https://content.openalex.org/works/W3089667743.grobid-xml"},"referenced_works_count":16,"referenced_works":["https://openalex.org/W602919348","https://openalex.org/W1975687818","https://openalex.org/W1989285461","https://openalex.org/W2010899207","https://openalex.org/W2063852316","https://openalex.org/W2066680775","https://openalex.org/W2078011285","https://openalex.org/W2090958186","https://openalex.org/W2099746488","https://openalex.org/W2125520394","https://openalex.org/W2136663834","https://openalex.org/W2157349031","https://openalex.org/W2171543997","https://openalex.org/W3121641555","https://openalex.org/W3123820027","https://openalex.org/W4232474910"],"related_works":["https://openalex.org/W3148528286","https://openalex.org/W1794622679","https://openalex.org/W2346495185","https://openalex.org/W3136966845","https://openalex.org/W1979589776","https://openalex.org/W3158734893","https://openalex.org/W3012080916","https://openalex.org/W2129956015","https://openalex.org/W3121401306","https://openalex.org/W2770144894","https://openalex.org/W2481729339","https://openalex.org/W2123362840","https://openalex.org/W588917471","https://openalex.org/W2962769750","https://openalex.org/W3143423650","https://openalex.org/W2250168847","https://openalex.org/W2531774139","https://openalex.org/W1107947989","https://openalex.org/W2373953412","https://openalex.org/W2292584306"],"abstract_inverted_index":{"This":[0],"paper":[1],"first":[2],"extends":[3],"some":[4,54,96,110,144],"well-known":[5],"univariate":[6],"stochastic":[7,12],"dominance":[8],"results":[9,160],"to":[10,23,36,44,73],"multivariate":[11],"dominances":[13],"(MSD)":[14],"for":[15,26,56,58,77,92,102,112,128],"both":[16,59,78,132],"risk":[17,20,60,63,79,82,103,106,133,136],"averters":[18,61,80,104,134],"and":[19,39,47,62,81,105,115,122,135,151,155],"seekers,":[21,83],"respectively,":[22],"n":[24,28],"order":[25],"any":[27],"\u2265":[29],"1":[30],"when":[31,147],"the":[32,40,74,88,100,124,129,153,156,159],"attributes":[33,148],"are":[34,71,149],"assumed":[35,43],"be":[37,45],"independent":[38],"utility":[41],"is":[42],"additively":[46],"separable.":[48],"Under":[49],"these":[50],"assumptions,":[51],"we":[52,67,142],"develop":[53,109,123],"properties":[55,111],"MSD":[57,70,101,121,127,145],"seekers.":[64,107],"For":[65],"example,":[66],"prove":[68],"that":[69,87],"equivalent":[72],"expected-utility":[75],"maximization":[76],"respectively.":[84],"We":[85,94,108],"show":[86],"hierarchical":[89],"relationship":[90],"exists":[91],"MSD.":[93],"establish":[95],"dual":[97],"relationships":[98,146],"between":[99],"non-negative":[113],"combinations":[114,117],"convex":[116],"random":[118],"variables":[119],"of":[120,126,131,158],"theory":[125],"preferences":[130],"seekers":[137],"on":[138],"diversification.":[139],"At":[140],"last,":[141],"discuss":[143,152],"dependent":[150],"importance":[154],"use":[157],"developed":[161],"in":[162],"this":[163],"paper.":[164]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":9},{"year":2017,"cited_by_count":5},{"year":2016,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}