{"id":"https://openalex.org/W4321608673","doi":"https://doi.org/10.1109/tac.2023.3244483","title":"Necessary and Sufficient Conditions for Pareto Optimal Solution of Backward Stochastic System With Application","display_name":"Necessary and Sufficient Conditions for Pareto Optimal Solution of Backward Stochastic System With Application","publication_year":2023,"publication_date":"2023-02-23","ids":{"openalex":"https://openalex.org/W4321608673","doi":"https://doi.org/10.1109/tac.2023.3244483"},"language":"en","primary_location":{"id":"doi:10.1109/tac.2023.3244483","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tac.2023.3244483","pdf_url":null,"source":{"id":"https://openalex.org/S184954342","display_name":"IEEE Transactions on Automatic Control","issn_l":"0018-9286","issn":["0018-9286","1558-2523","2334-3303"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Automatic Control","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/A5028267711","display_name":"Panpan Nie","orcid":"https://orcid.org/0000-0003-0827-1713"},"institutions":[{"id":"https://openalex.org/I154099455","display_name":"Shandong University","ror":"https://ror.org/0207yh398","country_code":"CN","type":"education","lineage":["https://openalex.org/I154099455"]},{"id":"https://openalex.org/I4210097715","display_name":"Qilu Normal University","ror":"https://ror.org/00wztsq19","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210097715"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Panpan Nie","raw_affiliation_strings":["School of Control Science and Engineering, Shandong University, Jinan, China","School of Information Science and Engineering, Qilu Normal University, Jinan, China"],"raw_orcid":"https://orcid.org/0000-0003-0827-1713","affiliations":[{"raw_affiliation_string":"School of Control Science and Engineering, Shandong University, Jinan, China","institution_ids":["https://openalex.org/I154099455"]},{"raw_affiliation_string":"School of Information Science and Engineering, Qilu Normal University, Jinan, China","institution_ids":["https://openalex.org/I4210097715"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5003684805","display_name":"Guangchen Wang","orcid":"https://orcid.org/0000-0002-7767-2476"},"institutions":[{"id":"https://openalex.org/I154099455","display_name":"Shandong University","ror":"https://ror.org/0207yh398","country_code":"CN","type":"education","lineage":["https://openalex.org/I154099455"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Guangchen Wang","raw_affiliation_strings":["School of Control Science and Engineering, Shandong University, Jinan, China"],"raw_orcid":"https://orcid.org/0000-0002-7767-2476","affiliations":[{"raw_affiliation_string":"School of Control Science and Engineering, Shandong University, Jinan, China","institution_ids":["https://openalex.org/I154099455"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5021869500","display_name":"Yu Wang","orcid":"https://orcid.org/0000-0003-0448-0489"},"institutions":[{"id":"https://openalex.org/I154099455","display_name":"Shandong University","ror":"https://ror.org/0207yh398","country_code":"CN","type":"education","lineage":["https://openalex.org/I154099455"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yu Wang","raw_affiliation_strings":["School of Control Science and Engineering, Shandong University, Jinan, China"],"raw_orcid":"https://orcid.org/0000-0003-0448-0489","affiliations":[{"raw_affiliation_string":"School of Control Science and Engineering, Shandong University, Jinan, China","institution_ids":["https://openalex.org/I154099455"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":2645,"currency":"USD","value_usd":2645},"apc_paid":null,"fwci":1.907,"has_fulltext":false,"cited_by_count":8,"citation_normalized_percentile":{"value":0.85546938,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"68","issue":"11","first_page":"6696","last_page":"6710"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10067","display_name":"Stochastic processes and financial applications","score":0.9988999962806702,"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":0.9988999962806702,"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/T11413","display_name":"Risk and Portfolio Optimization","score":0.9833999872207642,"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/T11110","display_name":"Stability and Controllability of Differential Equations","score":0.9746000170707703,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/differential-game","display_name":"Differential game","score":0.762549638748169},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.6498876810073853},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5705834627151489},{"id":"https://openalex.org/keywords/pareto-principle","display_name":"Pareto principle","score":0.5539796948432922},{"id":"https://openalex.org/keywords/optimal-control","display_name":"Optimal control","score":0.5461775064468384},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.42529192566871643},{"id":"https://openalex.org/keywords/pareto-optimal","display_name":"Pareto optimal","score":0.41593965888023376},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2845851480960846},{"id":"https://openalex.org/keywords/multi-objective-optimization","display_name":"Multi-objective optimization","score":0.2816781997680664}],"concepts":[{"id":"https://openalex.org/C2779006483","wikidata":"https://www.wikidata.org/wiki/Q1973196","display_name":"Differential game","level":2,"score":0.762549638748169},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.6498876810073853},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5705834627151489},{"id":"https://openalex.org/C137635306","wikidata":"https://www.wikidata.org/wiki/Q182667","display_name":"Pareto principle","level":2,"score":0.5539796948432922},{"id":"https://openalex.org/C91575142","wikidata":"https://www.wikidata.org/wiki/Q1971426","display_name":"Optimal control","level":2,"score":0.5461775064468384},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.42529192566871643},{"id":"https://openalex.org/C2986314615","wikidata":"https://www.wikidata.org/wiki/Q36829","display_name":"Pareto optimal","level":3,"score":0.41593965888023376},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2845851480960846},{"id":"https://openalex.org/C68781425","wikidata":"https://www.wikidata.org/wiki/Q2052203","display_name":"Multi-objective optimization","level":2,"score":0.2816781997680664},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tac.2023.3244483","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tac.2023.3244483","pdf_url":null,"source":{"id":"https://openalex.org/S184954342","display_name":"IEEE Transactions on Automatic Control","issn_l":"0018-9286","issn":["0018-9286","1558-2523","2334-3303"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Automatic Control","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G3680598195","display_name":null,"funder_award_id":"11831010","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G6755789306","display_name":null,"funder_award_id":"61925306","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G878655878","display_name":null,"funder_award_id":"61821004","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":28,"referenced_works":["https://openalex.org/W1594802219","https://openalex.org/W1976424144","https://openalex.org/W1982880509","https://openalex.org/W2005018490","https://openalex.org/W2021879117","https://openalex.org/W2068168851","https://openalex.org/W2070290218","https://openalex.org/W2078286993","https://openalex.org/W2078895915","https://openalex.org/W2089710246","https://openalex.org/W2092834085","https://openalex.org/W2095445700","https://openalex.org/W2095840799","https://openalex.org/W2110469502","https://openalex.org/W2122671188","https://openalex.org/W2157047632","https://openalex.org/W2157883119","https://openalex.org/W2499024707","https://openalex.org/W2751473477","https://openalex.org/W2807289721","https://openalex.org/W2891171846","https://openalex.org/W2896613176","https://openalex.org/W2979708496","https://openalex.org/W3036314310","https://openalex.org/W3089331246","https://openalex.org/W3119176801","https://openalex.org/W3125882718","https://openalex.org/W4212780424"],"related_works":["https://openalex.org/W1963790170","https://openalex.org/W2073298047","https://openalex.org/W2033790662","https://openalex.org/W2586328217","https://openalex.org/W2049264236","https://openalex.org/W317165722","https://openalex.org/W2728870795","https://openalex.org/W312725187","https://openalex.org/W4378499136","https://openalex.org/W1999828099"],"abstract_inverted_index":{"In":[0,50],"this":[1],"article,":[2],"we":[3],"are":[4,109],"interested":[5],"in":[6],"studying":[7],"a":[8,35,54,96,100],"new":[9],"kind":[10,101],"of":[11,16,25,37,45,65,91,102],"Pareto":[12,26,58],"cooperative":[13],"differential":[14,19,48],"game":[15,30,98],"backward":[17,46],"stochastic":[18,47],"equation.":[20],"Based":[21],"on":[22,88],"the":[23,29,51,75,89,92],"characterizations":[24],"optimal":[27,40,59,103],"solution,":[28],"problem":[31,108],"is":[32,61,72,78],"transformed":[33],"into":[34],"set":[36],"single":[38],"objective":[39],"control":[41],"problems":[42],"with":[43],"constraints":[44],"equations.":[49],"first":[52],"place,":[53],"necessary":[55,76],"condition":[56,77],"for":[57],"strategy":[60],"established":[62],"by":[63],"virtue":[64],"Ekeland's":[66],"variational":[67],"principle,":[68],"and":[69,99,105],"then,":[70],"it":[71],"proved":[73],"that":[74],"also":[79,110],"sufficient":[80],"under":[81],"certain":[82],"convex":[83],"assumption.":[84],"To":[85],"shed":[86],"light":[87],"application":[90],"abovementioned":[93],"theoretical":[94],"results,":[95],"linear\u2013quadratic":[97],"portfolio":[104],"consumption":[106],"selection":[107],"solved":[111],"explicitly.":[112]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":5},{"year":2023,"cited_by_count":1}],"updated_date":"2026-08-21T09:56:20.448147","created_date":"2025-10-10T00:00:00"}
