{"id":"https://openalex.org/W4414528737","doi":"https://doi.org/10.1080/1351847x.2025.2558114","title":"An end-to-end direct reinforcement learning approach for multi-factor based mean-variance portfolio optimization","display_name":"An end-to-end direct reinforcement learning approach for multi-factor based mean-variance portfolio optimization","publication_year":2025,"publication_date":"2025-09-25","ids":{"openalex":"https://openalex.org/W4414528737","doi":"https://doi.org/10.1080/1351847x.2025.2558114"},"language":"en","primary_location":{"id":"doi:10.1080/1351847x.2025.2558114","doi":"https://doi.org/10.1080/1351847x.2025.2558114","is_oa":false,"landing_page_url":"https://doi.org/10.1080/1351847x.2025.2558114","pdf_url":null,"source":{"id":"https://openalex.org/S82316188","display_name":"European Journal of Finance","issn_l":"1351-847X","issn":["1351-847X","1466-4364"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["abdc-a","anvur-class-a","anvur-scientific","cwts-core","fnege-3","jufo-1","norway-1","poland-70","russia-white-list-1","vabb-shw"],"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547","https://openalex.org/P4310320449"],"host_organization_lineage_names":["Taylor & Francis","Informa"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The European Journal of Finance","raw_type":"journal-article"},"volume":null,"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.2139/ssrn.4729683","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5015061573","display_name":"Ke Zhou","orcid":"https://orcid.org/0000-0002-2161-8796","observed_orcids":["https://orcid.org/0000-0002-2161-8796"]},"institutions":[{"id":"https://openalex.org/I16609230","display_name":"Hunan University","ror":"https://ror.org/05htk5m33","country_code":"CN","type":"education","lineage":["https://openalex.org/I16609230"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Ke Zhou","raw_affiliation_strings":["Hunan University","School of Business Administration, Hunan University, Changsha, People's Republic of China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Hunan University","institution_ids":["https://openalex.org/I16609230"]},{"raw_affiliation_string":"School of Business Administration, Hunan University, Changsha, People's Republic of China","institution_ids":["https://openalex.org/I16609230"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5114752434","display_name":"Xinman Huang","orcid":"https://orcid.org/0000-0002-8009-7441","observed_orcids":["https://orcid.org/0000-0002-8009-7441"]},"institutions":[{"id":"https://openalex.org/I16609230","display_name":"Hunan University","ror":"https://ror.org/05htk5m33","country_code":"CN","type":"education","lineage":["https://openalex.org/I16609230"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xinman Huang","raw_affiliation_strings":["Hunan University","School of Business Administration, Hunan University, Changsha, People's Republic of China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Hunan University","institution_ids":["https://openalex.org/I16609230"]},{"raw_affiliation_string":"School of Business Administration, Hunan University, Changsha, People's Republic of China","institution_ids":["https://openalex.org/I16609230"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5108908966","display_name":"Xinnan Chen","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I16609230","display_name":"Hunan University","ror":"https://ror.org/05htk5m33","country_code":"CN","type":"education","lineage":["https://openalex.org/I16609230"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xinnan Chen","raw_affiliation_strings":["Hunan University","School of Business Administration, Hunan University, Changsha, People's Republic of China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Hunan University","institution_ids":["https://openalex.org/I16609230"]},{"raw_affiliation_string":"School of Business Administration, Hunan University, Changsha, People's Republic of China","institution_ids":["https://openalex.org/I16609230"]}]},{"author_position":"last","author":{"id":null,"display_name":"Jianjun Gao","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I181679659","display_name":"Shanghai University of Finance and Economics","ror":"https://ror.org/00wtvfq62","country_code":"CN","type":"education","lineage":["https://openalex.org/I181679659"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Jianjun Gao","raw_affiliation_strings":["Shanghai University of Finance and Economics","School of Information Management and Engineering, Shanghai University of Finance and Economics, Shanghai, People's Republic of China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Shanghai University of Finance and Economics","institution_ids":["https://openalex.org/I181679659"]},{"raw_affiliation_string":"School of Information Management and Engineering, Shanghai University of Finance and Economics, Shanghai, People's Republic of China","institution_ids":["https://openalex.org/I181679659"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I181679659"],"apc_list":null,"apc_paid":null,"fwci":2.3483,"has_fulltext":false,"cited_by_count":4,"citation_normalized_percentile":{"value":0.89414124,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":97,"max":98},"biblio":{"volume":"32","issue":"4-6","first_page":"450","last_page":"481"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11413","display_name":"Risk and Portfolio Optimization","score":0.9545999765396118,"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"}},"topics":[{"id":"https://openalex.org/T11413","display_name":"Risk and Portfolio Optimization","score":0.9545999765396118,"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/T11326","display_name":"Stock Market Forecasting Methods","score":0.024399999529123306,"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/T10047","display_name":"Financial Markets and Investment Strategies","score":0.01269999984651804,"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/mean-variance-optimization","display_name":"mean-variance optimization","score":0.902999997138977},{"id":"https://openalex.org/keywords/multifactor-models","display_name":"multi-factor models","score":0.7540000081062317},{"id":"https://openalex.org/keywords/factor-loading-estimation","display_name":"factor loading estimation","score":0.8989999890327454},{"id":"https://openalex.org/keywords/out-of-sample-portfolio-performance","display_name":"out-of-sample portfolio performance","score":0.6949999928474426},{"id":"https://openalex.org/keywords/estimation-error","display_name":"estimation error","score":0.46299999952316284}],"concepts":[{"id":"https://openalex.org/C97541855","wikidata":"https://www.wikidata.org/wiki/Q830687","display_name":"Reinforcement learning","level":2,"score":0.597599983215332},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5663999915122986},{"id":"https://openalex.org/C2780821815","wikidata":"https://www.wikidata.org/wiki/Q5340806","display_name":"Portfolio","level":2,"score":0.45410001277923584},{"id":"https://openalex.org/C202655437","wikidata":"https://www.wikidata.org/wiki/Q7231728","display_name":"Portfolio optimization","level":3,"score":0.4027999937534332},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3797000050544739},{"id":"https://openalex.org/C98045186","wikidata":"https://www.wikidata.org/wiki/Q205663","display_name":"Process (computing)","level":2,"score":0.37630000710487366},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.36399999260902405},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.359499990940094},{"id":"https://openalex.org/C193254401","wikidata":"https://www.wikidata.org/wiki/Q2160088","display_name":"Robust optimization","level":2,"score":0.31189998984336853},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.3025999963283539},{"id":"https://openalex.org/C42475967","wikidata":"https://www.wikidata.org/wiki/Q194292","display_name":"Operations research","level":1,"score":0.2865999937057495},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.2842999994754791}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1080/1351847x.2025.2558114","doi":"https://doi.org/10.1080/1351847x.2025.2558114","is_oa":false,"landing_page_url":"https://doi.org/10.1080/1351847x.2025.2558114","pdf_url":null,"source":{"id":"https://openalex.org/S82316188","display_name":"European Journal of Finance","issn_l":"1351-847X","issn":["1351-847X","1466-4364"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["abdc-a","anvur-class-a","anvur-scientific","cwts-core","fnege-3","jufo-1","norway-1","poland-70","russia-white-list-1","vabb-shw"],"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547","https://openalex.org/P4310320449"],"host_organization_lineage_names":["Taylor & Francis","Informa"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The European Journal of Finance","raw_type":"journal-article"},{"id":"doi:10.2139/ssrn.4729683","doi":"https://doi.org/10.2139/ssrn.4729683","is_oa":true,"landing_page_url":"https://doi.org/10.2139/ssrn.4729683","pdf_url":null,"source":{"id":"https://openalex.org/S4210172589","display_name":"SSRN Electronic Journal","issn_l":"1556-5068","issn":["1556-5068"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I1318003438","host_organization_name":"RELX Group (Netherlands)","host_organization_lineage":["https://openalex.org/I1318003438"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":null,"raw_type":"posted-content"}],"best_oa_location":{"id":"doi:10.2139/ssrn.4729683","doi":"https://doi.org/10.2139/ssrn.4729683","is_oa":true,"landing_page_url":"https://doi.org/10.2139/ssrn.4729683","pdf_url":null,"source":{"id":"https://openalex.org/S4210172589","display_name":"SSRN Electronic Journal","issn_l":"1556-5068","issn":["1556-5068"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I1318003438","host_organization_name":"RELX Group (Netherlands)","host_organization_lineage":["https://openalex.org/I1318003438"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":null,"raw_type":"posted-content"},"sustainable_development_goals":[],"study_designs":[],"awards":[{"id":"https://openalex.org/G1047867184","display_name":"\u91d1\u878d\u51b3\u7b56\u6a21\u578b\u7684\u6cdb\u5316\u95ee\u9898\u7814\u7a76","funder_award_id":"71971132","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G2912422488","display_name":null,"funder_award_id":"72461160315","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"},{"id":"https://openalex.org/F4320321106","display_name":"Ministry of Education of the People's Republic of China","ror":"https://ror.org/01mv9t934"},{"id":"https://openalex.org/F4320324781","display_name":"Shanghai University of Finance and Economics","ror":"https://ror.org/00wtvfq62"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":66,"referenced_works":["https://openalex.org/W28519790","https://openalex.org/W41554520","https://openalex.org/W1977051850","https://openalex.org/W1995834279","https://openalex.org/W2018964251","https://openalex.org/W2062125287","https://openalex.org/W2069099760","https://openalex.org/W2073103707","https://openalex.org/W2073681337","https://openalex.org/W2105630053","https://openalex.org/W2127000676","https://openalex.org/W2163969674","https://openalex.org/W2169015875","https://openalex.org/W2344786740","https://openalex.org/W2592457170","https://openalex.org/W2597344944","https://openalex.org/W2625101268","https://openalex.org/W2737320136","https://openalex.org/W2766820687","https://openalex.org/W2799643291","https://openalex.org/W2896878316","https://openalex.org/W2917962335","https://openalex.org/W2938326684","https://openalex.org/W2947637889","https://openalex.org/W2969799658","https://openalex.org/W2970791107","https://openalex.org/W2997591727","https://openalex.org/W3003257820","https://openalex.org/W3003916820","https://openalex.org/W3032048943","https://openalex.org/W3083080466","https://openalex.org/W3085307128","https://openalex.org/W3112148262","https://openalex.org/W3116351249","https://openalex.org/W3121213159","https://openalex.org/W3121369525","https://openalex.org/W3122337495","https://openalex.org/W3123718809","https://openalex.org/W3124581837","https://openalex.org/W3125366755","https://openalex.org/W3125887435","https://openalex.org/W3130761309","https://openalex.org/W3160844106","https://openalex.org/W3182894621","https://openalex.org/W3196228797","https://openalex.org/W3202004693","https://openalex.org/W3206804449","https://openalex.org/W3215210492","https://openalex.org/W4205539948","https://openalex.org/W4214717370","https://openalex.org/W4225934559","https://openalex.org/W4226321685","https://openalex.org/W4230576380","https://openalex.org/W4231934021","https://openalex.org/W4232474910","https://openalex.org/W4233197277","https://openalex.org/W4244246377","https://openalex.org/W4248510338","https://openalex.org/W4253377838","https://openalex.org/W4290725190","https://openalex.org/W4306935481","https://openalex.org/W4362722548","https://openalex.org/W4379933502","https://openalex.org/W4388492808","https://openalex.org/W4390968402","https://openalex.org/W4394998532"],"related_works":["https://openalex.org/W4392844688","https://openalex.org/W4410887149","https://openalex.org/W7118797121","https://openalex.org/W4412195317","https://openalex.org/W4319660349","https://openalex.org/W4320713061","https://openalex.org/W7051833205","https://openalex.org/W3123064686","https://openalex.org/W4402118037","https://openalex.org/W4285235657"],"abstract_inverted_index":{"This":[0,58],"paper":[1],"introduces":[2],"an":[3,140],"end-to-end":[4],"online":[5,55,141],"portfolio":[6,24,34,111,117,156,160],"decision":[7,56],"model":[8,20],"within":[9],"the":[10,18,64,72,80,99,104,109,115,120,131,135,146,159,169],"framework":[11],"of":[12,79,106],"direct":[13],"reinforcement":[14],"learning,":[15],"seamlessly":[16],"integrating":[17],"multi-factor":[19],"and":[21,33,83,97],"mean-variance":[22],"(MV)":[23],"optimization.":[25],"Recognizing":[26],"that":[27,182],"classical":[28],"methods,":[29],"which":[30],"separate":[31],"estimation":[32,42],"optimization":[35,112,161],"into":[36,52],"a":[37,53,77,90,201],"two-step":[38],"scheme,":[39],"may":[40],"accumulate":[41],"errors":[43],"jeopardizing":[44],"overall":[45],"performance,":[46],"our":[47,183],"approach":[48,184],"unifies":[49],"these":[50,188],"steps":[51],"performance-oriented":[54],"process.":[57],"integration":[59],"is":[60,195],"achieved":[61],"by":[62,150],"tuning":[63],"neural":[65,91],"network":[66,92,124],"parameters":[67,125],"directly":[68],"with":[69,128],"respect":[70,129],"to":[71,93,130,198],"reward":[73,133],"function,":[74],"designed":[75],"as":[76],"combination":[78],"prediction":[81],"error":[82],"realized":[84,121],"MV":[85,110,155],"utility.":[86,122],"Specifically,":[87],"we":[88,167],"employ":[89],"estimate":[94],"future":[95],"returns":[96],"generate":[98],"factor":[100,199],"loading":[101],"matrix,":[102],"enabling":[103],"computation":[105],"inputs":[107],"for":[108,144,154,204],"model.":[113],"Implementing":[114],"resulting":[116],"further":[118],"provides":[119],"The":[123,179],"are":[126],"optimized":[127],"updated":[132],"using":[134],"gradient":[136,147],"method.":[137],"We":[138],"develop":[139],"updating":[142],"scheme":[143],"computing":[145],"in":[148,176],"backpropagation":[149],"providing":[151],"explicit":[152],"formulas":[153],"derivatives":[157],"through":[158],"layer.":[162],"Utilizing":[163],"real":[164],"market":[165],"data,":[166],"evaluate":[168],"proposed":[170],"method":[171],"against":[172],"several":[173],"benchmark":[174],"portfolios":[175],"out-of-sample":[177],"tests.":[178],"experiments":[180],"demonstrate":[181],"not":[185],"only":[186],"outperforms":[187],"benchmarks":[189],"across":[190],"various":[191],"performance":[192],"metrics":[193],"but":[194],"also":[196],"transparent":[197],"analysis,":[200],"favorable":[202],"trait":[203],"practitioners.":[205]},"counts_by_year":[{"year":2026,"cited_by_count":4}],"updated_date":"2026-11-04T10:54:05.112534","created_date":"2025-10-10T00:00:00"}
