{"id":"https://openalex.org/W1981768388","doi":"https://doi.org/10.1137/080742889","title":"Continuous-Time Markowitz's Model with Transaction Costs","display_name":"Continuous-Time Markowitz's Model with Transaction Costs","publication_year":2010,"publication_date":"2010-01-01","ids":{"openalex":"https://openalex.org/W1981768388","doi":"https://doi.org/10.1137/080742889","mag":"1981768388"},"language":"en","primary_location":{"id":"doi:10.1137/080742889","is_oa":false,"landing_page_url":"https://doi.org/10.1137/080742889","pdf_url":null,"source":{"id":"https://openalex.org/S75627377","display_name":"SIAM Journal on Financial Mathematics","issn_l":"1945-497X","issn":["1945-497X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Financial Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/0906.0678","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5077020574","display_name":"Min Dai","orcid":"https://orcid.org/0000-0002-8270-9413"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Min Dai","raw_affiliation_strings":["matdm@nus.edu.sg#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"matdm@nus.edu.sg#TAB#","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5019266386","display_name":"Zuo Quan Xu","orcid":"https://orcid.org/0000-0001-6824-1634"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Zuo Quan Xu","raw_affiliation_strings":["xuz@maths.ox.ac.uk#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"xuz@maths.ox.ac.uk#TAB#","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5109487227","display_name":"Xun Yu Zhou","orcid":"https://orcid.org/0000-0001-9908-5697"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Xun Yu Zhou","raw_affiliation_strings":["zhouxy@maths.ox.ac.uk#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"zhouxy@maths.ox.ac.uk#TAB#","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":4.8818,"has_fulltext":false,"cited_by_count":77,"citation_normalized_percentile":{"value":0.94855358,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"1","issue":"1","first_page":"96","last_page":"125"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10067","display_name":"Stochastic processes and financial applications","score":0.9990000128746033,"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":0.9990000128746033,"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/T10047","display_name":"Financial Markets and Investment Strategies","score":0.9968000054359436,"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/T12137","display_name":"Economic theories and models","score":0.9943000078201294,"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/transaction-cost","display_name":"Transaction cost","score":0.6576244831085205},{"id":"https://openalex.org/keywords/stock","display_name":"Stock (firearms)","score":0.5940437912940979},{"id":"https://openalex.org/keywords/portfolio","display_name":"Portfolio","score":0.5460588335990906},{"id":"https://openalex.org/keywords/economics","display_name":"Economics","score":0.5361990928649902},{"id":"https://openalex.org/keywords/time-horizon","display_name":"Time horizon","score":0.515637993812561},{"id":"https://openalex.org/keywords/bond","display_name":"Bond","score":0.4742392897605896},{"id":"https://openalex.org/keywords/expected-return","display_name":"Expected return","score":0.44193100929260254},{"id":"https://openalex.org/keywords/stochastic-control","display_name":"Stochastic control","score":0.44001075625419617},{"id":"https://openalex.org/keywords/volatility","display_name":"Volatility (finance)","score":0.4291529655456543},{"id":"https://openalex.org/keywords/econometrics","display_name":"Econometrics","score":0.4286348521709442},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3433288335800171},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.33035898208618164},{"id":"https://openalex.org/keywords/microeconomics","display_name":"Microeconomics","score":0.32268816232681274},{"id":"https://openalex.org/keywords/financial-economics","display_name":"Financial economics","score":0.31823062896728516},{"id":"https://openalex.org/keywords/optimal-control","display_name":"Optimal control","score":0.2728669047355652},{"id":"https://openalex.org/keywords/finance","display_name":"Finance","score":0.16942399740219116}],"concepts":[{"id":"https://openalex.org/C98965940","wikidata":"https://www.wikidata.org/wiki/Q877496","display_name":"Transaction cost","level":2,"score":0.6576244831085205},{"id":"https://openalex.org/C204036174","wikidata":"https://www.wikidata.org/wiki/Q909380","display_name":"Stock (firearms)","level":2,"score":0.5940437912940979},{"id":"https://openalex.org/C2780821815","wikidata":"https://www.wikidata.org/wiki/Q5340806","display_name":"Portfolio","level":2,"score":0.5460588335990906},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.5361990928649902},{"id":"https://openalex.org/C28761237","wikidata":"https://www.wikidata.org/wiki/Q7805321","display_name":"Time horizon","level":2,"score":0.515637993812561},{"id":"https://openalex.org/C69738904","wikidata":"https://www.wikidata.org/wiki/Q11693","display_name":"Bond","level":2,"score":0.4742392897605896},{"id":"https://openalex.org/C154611145","wikidata":"https://www.wikidata.org/wiki/Q4331879","display_name":"Expected return","level":3,"score":0.44193100929260254},{"id":"https://openalex.org/C170131372","wikidata":"https://www.wikidata.org/wiki/Q7617811","display_name":"Stochastic control","level":3,"score":0.44001075625419617},{"id":"https://openalex.org/C91602232","wikidata":"https://www.wikidata.org/wiki/Q756115","display_name":"Volatility (finance)","level":2,"score":0.4291529655456543},{"id":"https://openalex.org/C149782125","wikidata":"https://www.wikidata.org/wiki/Q160039","display_name":"Econometrics","level":1,"score":0.4286348521709442},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3433288335800171},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.33035898208618164},{"id":"https://openalex.org/C175444787","wikidata":"https://www.wikidata.org/wiki/Q39072","display_name":"Microeconomics","level":1,"score":0.32268816232681274},{"id":"https://openalex.org/C106159729","wikidata":"https://www.wikidata.org/wiki/Q2294553","display_name":"Financial economics","level":1,"score":0.31823062896728516},{"id":"https://openalex.org/C91575142","wikidata":"https://www.wikidata.org/wiki/Q1971426","display_name":"Optimal control","level":2,"score":0.2728669047355652},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.16942399740219116},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C78519656","wikidata":"https://www.wikidata.org/wiki/Q101333","display_name":"Mechanical engineering","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1137/080742889","is_oa":false,"landing_page_url":"https://doi.org/10.1137/080742889","pdf_url":null,"source":{"id":"https://openalex.org/S75627377","display_name":"SIAM Journal on Financial Mathematics","issn_l":"1945-497X","issn":["1945-497X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Financial Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:0906.0678","is_oa":true,"landing_page_url":"http://arxiv.org/abs/0906.0678","pdf_url":"https://arxiv.org/pdf/0906.0678","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"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:scholarbank.nus.edu.sg:10635/103061","is_oa":false,"landing_page_url":"http://scholarbank.nus.edu.sg/handle/10635/103061","pdf_url":null,"source":{"id":"https://openalex.org/S7407052290","display_name":"National University of Singapore","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":"Scopus","raw_type":"Article"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:0906.0678","is_oa":true,"landing_page_url":"http://arxiv.org/abs/0906.0678","pdf_url":"https://arxiv.org/pdf/0906.0678","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"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"},"sustainable_development_goals":[{"display_name":"Partnerships for the goals","id":"https://metadata.un.org/sdg/17","score":0.46000000834465027}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":57,"referenced_works":["https://openalex.org/W299346747","https://openalex.org/W1518792628","https://openalex.org/W1525883337","https://openalex.org/W1558902221","https://openalex.org/W1577527822","https://openalex.org/W1580561995","https://openalex.org/W1583323312","https://openalex.org/W1664871661","https://openalex.org/W1967495257","https://openalex.org/W1970030120","https://openalex.org/W1975765664","https://openalex.org/W1976352744","https://openalex.org/W1984697146","https://openalex.org/W1988916339","https://openalex.org/W2002788332","https://openalex.org/W2003943366","https://openalex.org/W2016864253","https://openalex.org/W2021355027","https://openalex.org/W2041823389","https://openalex.org/W2042775870","https://openalex.org/W2044400665","https://openalex.org/W2046904024","https://openalex.org/W2050593112","https://openalex.org/W2059339817","https://openalex.org/W2059627964","https://openalex.org/W2065030872","https://openalex.org/W2077216271","https://openalex.org/W2077791698","https://openalex.org/W2079348087","https://openalex.org/W2099190203","https://openalex.org/W2102063802","https://openalex.org/W2108971159","https://openalex.org/W2114102890","https://openalex.org/W2115580984","https://openalex.org/W2125067373","https://openalex.org/W2126373180","https://openalex.org/W2132621139","https://openalex.org/W2132857164","https://openalex.org/W2134306794","https://openalex.org/W2141858721","https://openalex.org/W2144846366","https://openalex.org/W2169417293","https://openalex.org/W2175456627","https://openalex.org/W2331890423","https://openalex.org/W2361440531","https://openalex.org/W3027820740","https://openalex.org/W3106108365","https://openalex.org/W3121153783","https://openalex.org/W3123572594","https://openalex.org/W3123697738","https://openalex.org/W3124574885","https://openalex.org/W3124656020","https://openalex.org/W3125997527","https://openalex.org/W4206606494","https://openalex.org/W4210791600","https://openalex.org/W4229928878","https://openalex.org/W4292083418"],"related_works":["https://openalex.org/W1536727859","https://openalex.org/W3124009333","https://openalex.org/W2417737453","https://openalex.org/W2373220065","https://openalex.org/W2233476005","https://openalex.org/W2089073576","https://openalex.org/W3125714252","https://openalex.org/W2341580512","https://openalex.org/W4220772402","https://openalex.org/W1986042399"],"abstract_inverted_index":{"A":[0],"continuous-time":[1],"Markowitz's":[2],"mean-variance":[3],"portfolio":[4],"selection":[5],"problem":[6,40,51],"is":[7,22,41,123,134,171,197,219,248,266],"studied":[8],"in":[9,52,78,81,131,178,190],"a":[10,23,30,35,44,49,88,97,128],"market":[11],"with":[12,29,255],"one":[13,15,92],"stock,":[14],"bond,":[16],"and":[17,54,70,153,237],"proportional":[18],"transaction":[19,145,182],"costs.":[20],"This":[21,80],"singular":[24],"stochastic":[25],"control":[26],"problem,":[27,48,90],"inherently":[28],"finite":[31],"time":[32,216],"horizon.":[33],"Via":[34],"series":[36],"of":[37,108,149,181,194,270],"transformations,":[38],"the":[39,67,84,103,109,137,144,150,154,168,179,203,209,212,215,222,227,235,242,245,256,263,271],"turned":[42],"into":[43],"so-called":[45],"double":[46],"obstacle":[47],"well-studied":[50],"physics":[53],"PDE":[55],"literature,":[56],"featuring":[57],"two":[58,63],"time-varying":[59],"free":[60],"boundaries.":[61],"The":[62],"boundaries,":[64],"which":[65,133],"define":[66],"buy,":[68],"sell,":[69],"no-trade":[71,104],"regions,":[72],"are":[73,112,115],"proved":[74],"to":[75,95,217,233,240],"be":[76,165,188,230],"smooth":[77],"time.":[79],"turn":[82],"characterizes":[83],"optimal":[85,110,204],"strategy,":[86],"via":[87],"Skorokhod":[89],"as":[91,141,143],"that":[93,114,125,158,174,200,262],"tries":[94],"keep":[96],"certain":[98],"adjusted":[99],"bond-stock":[100],"position":[101],"within":[102],"region.":[105],"Several":[106],"features":[107],"strategy":[111,205],"revealed":[113],"remarkably":[116],"different":[117],"from":[118],"its":[119],"no-transaction-cost":[120],"counterpart.":[121],"It":[122,196],"shown":[124],"there":[126],"exists":[127],"critical":[129,175,224],"length":[130,176],"time,":[132],"dependent":[135],"on":[136],"stock":[138,155,210,236,243],"excess":[139],"return":[140,162,186],"well":[142],"fees":[146],"but":[147],"independent":[148],"investment":[151,259,272],"target":[152],"volatility,":[156],"so":[157],"an":[159,191,267],"expected":[160,185],"terminal":[161],"may":[163],"not":[164,207],"achievable":[166],"if":[167],"planning":[169,264],"horizon":[170,265],"shorter":[172,220],"than":[173,221],"(while":[177],"absence":[180],"costs":[183],"any":[184],"can":[187],"reached":[189],"arbitrary":[192],"period":[193],"time).":[195],"further":[198],"demonstrated":[199],"anyone":[201],"following":[202],"should":[206],"buy":[208,234],"beyond":[211],"point":[213],"when":[214,244],"maturity":[218,246],"aforementioned":[223],"length.":[225],"Moreover,":[226],"investor":[228],"would":[229],"less":[231],"likely":[232,239],"more":[238],"sell":[241],"date":[247],"getting":[249],"closer.":[250],"These":[251],"features,":[252],"while":[253],"consistent":[254],"widely":[257],"accepted":[258],"wisdom,":[260],"suggest":[261],"integral":[268],"part":[269],"opportunities.":[273]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":7},{"year":2023,"cited_by_count":7},{"year":2022,"cited_by_count":12},{"year":2021,"cited_by_count":7},{"year":2020,"cited_by_count":6},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":5},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":9},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":6},{"year":2012,"cited_by_count":4}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}