{"id":"https://openalex.org/W4413242903","doi":"https://doi.org/10.1287/opre.2022.0160","title":"Optimal Trading with Speed-Dependent Transaction Cost Rates: A Flexible Framework","display_name":"Optimal Trading with Speed-Dependent Transaction Cost Rates: A Flexible Framework","publication_year":2025,"publication_date":"2025-08-08","ids":{"openalex":"https://openalex.org/W4413242903","doi":"https://doi.org/10.1287/opre.2022.0160"},"language":"en","primary_location":{"id":"doi:10.1287/opre.2022.0160","is_oa":false,"landing_page_url":"https://doi.org/10.1287/opre.2022.0160","pdf_url":null,"source":{"id":"https://openalex.org/S125775545","display_name":"Operations Research","issn_l":"0030-364X","issn":["0030-364X","1526-5463"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315699","host_organization_name":"Institute for Operations Research and the Management Sciences","host_organization_lineage":["https://openalex.org/P4310315699"],"host_organization_lineage_names":["Institute for Operations Research and the Management Sciences"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Operations Research","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/A5100410355","display_name":"Hong Liu","orcid":"https://orcid.org/0000-0003-1904-6001"},"institutions":[{"id":"https://openalex.org/I204465549","display_name":"Washington University in St. Louis","ror":"https://ror.org/01yc7t268","country_code":"US","type":"education","lineage":["https://openalex.org/I204465549"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Hong Liu","raw_affiliation_strings":["Washington University in St. Louis, St. Louis, Missouri 63130; and FISF, Shanghai 200433, China"],"raw_orcid":"https://orcid.org/0000-0003-1904-6001","affiliations":[{"raw_affiliation_string":"Washington University in St. Louis, St. Louis, Missouri 63130; and FISF, Shanghai 200433, China","institution_ids":["https://openalex.org/I204465549"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5010720507","display_name":"Shuaijie Qian","orcid":"https://orcid.org/0000-0003-2692-4845"},"institutions":[{"id":"https://openalex.org/I200769079","display_name":"Hong Kong University of Science and Technology","ror":"https://ror.org/00q4vv597","country_code":"HK","type":"education","lineage":["https://openalex.org/I200769079"]}],"countries":["HK"],"is_corresponding":false,"raw_author_name":"Shuaijie Qian","raw_affiliation_strings":["Department of Mathematics, Hong Kong University of Science and Technology, Hong Kong, China"],"raw_orcid":"https://orcid.org/0000-0003-2692-4845","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Hong Kong University of Science and Technology, Hong Kong, China","institution_ids":["https://openalex.org/I200769079"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5101718352","display_name":"Jing Xu","orcid":"https://orcid.org/0000-0002-4352-7756"},"institutions":[{"id":"https://openalex.org/I78988378","display_name":"Renmin University of China","ror":"https://ror.org/041pakw92","country_code":"CN","type":"education","lineage":["https://openalex.org/I78988378"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jing Xu","raw_affiliation_strings":["School of Finance, Renmin University of China, Beijing 100872, China"],"raw_orcid":"https://orcid.org/0000-0002-4352-7756","affiliations":[{"raw_affiliation_string":"School of Finance, Renmin University of China, Beijing 100872, China","institution_ids":["https://openalex.org/I78988378"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.27756629,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"73","issue":"6","first_page":"2933","last_page":"2952"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12137","display_name":"Economic theories and models","score":0.9944000244140625,"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"}},"topics":[{"id":"https://openalex.org/T12137","display_name":"Economic theories and models","score":0.9944000244140625,"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"}},{"id":"https://openalex.org/T10047","display_name":"Financial Markets and Investment Strategies","score":0.9918000102043152,"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/T11270","display_name":"Complex Systems and Time Series Analysis","score":0.9871000051498413,"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/piecewise-linear-function","display_name":"Piecewise linear function","score":0.6807329058647156},{"id":"https://openalex.org/keywords/transaction-cost","display_name":"Transaction cost","score":0.6680669784545898},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.644166111946106},{"id":"https://openalex.org/keywords/piecewise","display_name":"Piecewise","score":0.6329681277275085},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.5794975757598877},{"id":"https://openalex.org/keywords/trading-strategy","display_name":"Trading strategy","score":0.5630502104759216},{"id":"https://openalex.org/keywords/database-transaction","display_name":"Database transaction","score":0.5615952014923096},{"id":"https://openalex.org/keywords/limit","display_name":"Limit (mathematics)","score":0.558241605758667},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.5564824342727661},{"id":"https://openalex.org/keywords/position","display_name":"Position (finance)","score":0.48983070254325867},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.4584810733795166},{"id":"https://openalex.org/keywords/econometrics","display_name":"Econometrics","score":0.21199440956115723},{"id":"https://openalex.org/keywords/microeconomics","display_name":"Microeconomics","score":0.1765117049217224},{"id":"https://openalex.org/keywords/economics","display_name":"Economics","score":0.17197468876838684},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.16897916793823242},{"id":"https://openalex.org/keywords/finance","display_name":"Finance","score":0.07760503888130188}],"concepts":[{"id":"https://openalex.org/C17095337","wikidata":"https://www.wikidata.org/wiki/Q2375229","display_name":"Piecewise linear function","level":2,"score":0.6807329058647156},{"id":"https://openalex.org/C98965940","wikidata":"https://www.wikidata.org/wiki/Q877496","display_name":"Transaction cost","level":2,"score":0.6680669784545898},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.644166111946106},{"id":"https://openalex.org/C164660894","wikidata":"https://www.wikidata.org/wiki/Q2037833","display_name":"Piecewise","level":2,"score":0.6329681277275085},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.5794975757598877},{"id":"https://openalex.org/C131562839","wikidata":"https://www.wikidata.org/wiki/Q1574928","display_name":"Trading strategy","level":2,"score":0.5630502104759216},{"id":"https://openalex.org/C75949130","wikidata":"https://www.wikidata.org/wiki/Q848010","display_name":"Database transaction","level":2,"score":0.5615952014923096},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.558241605758667},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.5564824342727661},{"id":"https://openalex.org/C198082294","wikidata":"https://www.wikidata.org/wiki/Q3399648","display_name":"Position (finance)","level":2,"score":0.48983070254325867},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4584810733795166},{"id":"https://openalex.org/C149782125","wikidata":"https://www.wikidata.org/wiki/Q160039","display_name":"Econometrics","level":1,"score":0.21199440956115723},{"id":"https://openalex.org/C175444787","wikidata":"https://www.wikidata.org/wiki/Q39072","display_name":"Microeconomics","level":1,"score":0.1765117049217224},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.17197468876838684},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.16897916793823242},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.07760503888130188},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"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/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1287/opre.2022.0160","is_oa":false,"landing_page_url":"https://doi.org/10.1287/opre.2022.0160","pdf_url":null,"source":{"id":"https://openalex.org/S125775545","display_name":"Operations Research","issn_l":"0030-364X","issn":["0030-364X","1526-5463"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315699","host_organization_name":"Institute for Operations Research and the Management Sciences","host_organization_lineage":["https://openalex.org/P4310315699"],"host_organization_lineage_names":["Institute for Operations Research and the Management Sciences"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Operations Research","raw_type":"journal-article"},{"id":"pmh:oai:repository.hkust.edu.hk:1783.1-167362","is_oa":false,"landing_page_url":"http://repository.hkust.edu.hk/ir/Record/1783.1-167362","pdf_url":null,"source":{"id":"https://openalex.org/S4306401796","display_name":"Rare & Special e-Zone (The Hong Kong University of Science and Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I200769079","host_organization_name":"Hong Kong University of Science and Technology","host_organization_lineage":["https://openalex.org/I200769079"],"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":"Article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":45,"referenced_works":["https://openalex.org/W1557794357","https://openalex.org/W1863029622","https://openalex.org/W1910594934","https://openalex.org/W1929167035","https://openalex.org/W1975158891","https://openalex.org/W1976352744","https://openalex.org/W1976592774","https://openalex.org/W1985018066","https://openalex.org/W1988270113","https://openalex.org/W2001770658","https://openalex.org/W2003486631","https://openalex.org/W2005158847","https://openalex.org/W2041346007","https://openalex.org/W2063427656","https://openalex.org/W2074524292","https://openalex.org/W2095693698","https://openalex.org/W2095913825","https://openalex.org/W2097372502","https://openalex.org/W2115185486","https://openalex.org/W2115580984","https://openalex.org/W2125067373","https://openalex.org/W2143173505","https://openalex.org/W2148216043","https://openalex.org/W2153332182","https://openalex.org/W2155792697","https://openalex.org/W2159161803","https://openalex.org/W2163139939","https://openalex.org/W2168038988","https://openalex.org/W2171217792","https://openalex.org/W2324041629","https://openalex.org/W2402405276","https://openalex.org/W2413884937","https://openalex.org/W3023274588","https://openalex.org/W3121394145","https://openalex.org/W3121397555","https://openalex.org/W3121581126","https://openalex.org/W3121617675","https://openalex.org/W3122267193","https://openalex.org/W3123177402","https://openalex.org/W3123718809","https://openalex.org/W3123781324","https://openalex.org/W3124099220","https://openalex.org/W3124729273","https://openalex.org/W3125210341","https://openalex.org/W3126039549"],"related_works":["https://openalex.org/W1536727859","https://openalex.org/W3124009333","https://openalex.org/W2133947431","https://openalex.org/W2490196280","https://openalex.org/W3182827720","https://openalex.org/W1596838019","https://openalex.org/W3208509670","https://openalex.org/W2109304297","https://openalex.org/W2100864966","https://openalex.org/W2083709218"],"abstract_inverted_index":{"Optimal":[0],"Trading":[1,41],"with":[2,42,63],"Flexible":[3,48],"Speed-Dependent":[4,43],"Transaction":[5,7,44],"Costs":[6],"cost":[8],"rates":[9],"(TCRs)":[10],"implied":[11],"by":[12],"most":[13],"limit":[14],"order":[15],"books":[16],"(LOBs)":[17],"display":[18],"irregular":[19],"functional":[20],"forms":[21],"in":[22,36,73],"trading":[23,89,98,113,117],"speeds,":[24],"making":[25],"it":[26],"difficult":[27],"to":[28,58],"fit":[29],"them":[30],"using":[31],"the":[32,74,87,106,119],"TCR":[33,65,70,79,131],"functions":[34],"proposed":[35],"prior":[37],"studies.":[38],"In":[39,104],"\u201cOptimal":[40],"Cost":[45],"Rates:":[46],"A":[47],"Framework,\u201d":[49],"Liu,":[50],"Qian,":[51],"and":[52,96],"Xu":[53],"develop":[54],"a":[55,124],"workhorse":[56],"model":[57,75,92],"study":[59],"optimal":[60,88],"trade":[61],"execution":[62],"general":[64],"functions.":[66,80],"The":[67,81,91],"piecewise":[68],"linear":[69,130],"function":[71],"form":[72],"can":[76,133],"approximate":[77],"any":[78],"authors":[82,107],"characterize":[83],"important":[84],"features":[85],"of":[86],"strategy.":[90],"simultaneously":[93],"generates":[94],"order-shredding":[95],"U-shape":[97],"patterns":[99],"for":[100],"large":[101],"required":[102],"trades.":[103],"addition,":[105],"demonstrate":[108],"that":[109],"implementing":[110],"common":[111],"naive":[112],"strategies,":[114],"such":[115],"as":[116],"all":[118],"position":[120],"instantly,":[121],"or":[122,127],"at":[123],"constant":[125],"speed,":[126],"incorrectly":[128],"assuming":[129],"function,":[132],"be":[134],"costly.":[135]},"counts_by_year":[],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}
