{"id":"https://openalex.org/W7213310225","doi":"https://doi.org/10.48550/arxiv.2609.15901","title":"Strategic Index Reconstitution: Differential Games, Closed-Loop Equilibria and Mean-Field Dynamics","display_name":"Strategic Index Reconstitution: Differential Games, Closed-Loop Equilibria and Mean-Field Dynamics","publication_year":2026,"publication_date":"2026-09-14","ids":{"openalex":"https://openalex.org/W7213310225","doi":"https://doi.org/10.48550/arxiv.2609.15901"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.15901","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.15901","pdf_url":"https://arxiv.org/pdf/2609.15901","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2609.15901","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5151731709","display_name":"Lukas-Benedikt Fiechtner","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I97018004","display_name":"Stanford University","ror":"https://ror.org/00f54p054","country_code":"US","type":"education","lineage":["https://openalex.org/I97018004"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Fiechtner, Lukas-Benedikt","raw_affiliation_strings":["Institute for Computational and Mathematical Engineering , Stanford University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute for Computational and Mathematical Engineering , Stanford University","institution_ids":["https://openalex.org/I97018004"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5011147039","display_name":"Jos\u00e9 Blanchet","orcid":"https://orcid.org/0000-0001-5895-0912","observed_orcids":["https://orcid.org/0000-0001-5895-0912"]},"institutions":[{"id":"https://openalex.org/I97018004","display_name":"Stanford University","ror":"https://ror.org/00f54p054","country_code":"US","type":"education","lineage":["https://openalex.org/I97018004"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Blanchet, Jose","raw_affiliation_strings":["Department of Management Science and Engineering , Stanford University","Institute for Computational and Mathematical Engineering , Stanford University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Management Science and Engineering , Stanford University","institution_ids":["https://openalex.org/I97018004"]},{"raw_affiliation_string":"Institute for Computational and Mathematical Engineering , Stanford University","institution_ids":["https://openalex.org/I97018004"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I97018004"],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10067","display_name":"Stochastic processes and financial applications","score":0.9394999742507935,"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":0.9394999742507935,"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":0.056699998676776886,"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/T11031","display_name":"Game Theory and Applications","score":0.000699999975040555,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/index-reconstitution","display_name":"index reconstitution","score":0.9240000247955322},{"id":"https://openalex.org/keywords/index-rebalancing","display_name":"index rebalancing","score":0.6740000247955322},{"id":"https://openalex.org/keywords/opportunistic-trading","display_name":"opportunistic trading","score":0.843999981880188},{"id":"https://openalex.org/keywords/differential-games","display_name":"differential games","score":0.7049999833106995},{"id":"https://openalex.org/keywords/mean-field-dynamics","display_name":"mean-field dynamics","score":0.7450000047683716},{"id":"https://openalex.org/keywords/subgame-perfect-equilibrium","display_name":"subgame perfect equilibrium","score":0.8769999742507935},{"id":"https://openalex.org/keywords/matrix-riccati-equation","display_name":"matrix Riccati equation","score":0.9229999780654907},{"id":"https://openalex.org/keywords/market-impact","display_name":"price impact","score":0.6430000066757202},{"id":"https://openalex.org/keywords/execution-cost","display_name":"execution cost","score":0.9419999718666077},{"id":"https://openalex.org/keywords/implementation-shortfall","display_name":"implementation shortfall","score":0.7440000176429749},{"id":"https://openalex.org/keywords/belief-dispersion","display_name":"belief dispersion","score":0.8109999895095825},{"id":"https://openalex.org/keywords/trading-volume","display_name":"trading volume","score":0.5609999895095825}],"concepts":[{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.5795000195503235},{"id":"https://openalex.org/C46814582","wikidata":"https://www.wikidata.org/wiki/Q23389","display_name":"Nash equilibrium","level":2,"score":0.5605999827384949},{"id":"https://openalex.org/C2777382242","wikidata":"https://www.wikidata.org/wiki/Q6017816","display_name":"Index (typography)","level":2,"score":0.5490000247955322},{"id":"https://openalex.org/C198082294","wikidata":"https://www.wikidata.org/wiki/Q3399648","display_name":"Position (finance)","level":2,"score":0.492900013923645},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4749999940395355},{"id":"https://openalex.org/C144237770","wikidata":"https://www.wikidata.org/wiki/Q747534","display_name":"Mathematical economics","level":1,"score":0.460099995136261},{"id":"https://openalex.org/C2779006483","wikidata":"https://www.wikidata.org/wiki/Q1973196","display_name":"Differential game","level":2,"score":0.45159998536109924},{"id":"https://openalex.org/C4679612","wikidata":"https://www.wikidata.org/wiki/Q866298","display_name":"Aggregate (composite)","level":2,"score":0.4478999972343445},{"id":"https://openalex.org/C51544822","wikidata":"https://www.wikidata.org/wiki/Q465274","display_name":"Ordinary differential equation","level":3,"score":0.44620001316070557},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.43709999322891235},{"id":"https://openalex.org/C2780801425","wikidata":"https://www.wikidata.org/wiki/Q5164392","display_name":"Construct (python library)","level":2,"score":0.42829999327659607},{"id":"https://openalex.org/C149782125","wikidata":"https://www.wikidata.org/wiki/Q160039","display_name":"Econometrics","level":1,"score":0.420199990272522},{"id":"https://openalex.org/C92757383","wikidata":"https://www.wikidata.org/wiki/Q382497","display_name":"Affine transformation","level":2,"score":0.39259999990463257},{"id":"https://openalex.org/C2780964549","wikidata":"https://www.wikidata.org/wiki/Q5156353","display_name":"Competitive equilibrium","level":2,"score":0.3905999958515167},{"id":"https://openalex.org/C93226319","wikidata":"https://www.wikidata.org/wiki/Q193137","display_name":"Differential (mechanical device)","level":2,"score":0.3824999928474426},{"id":"https://openalex.org/C107551265","wikidata":"https://www.wikidata.org/wiki/Q1458245","display_name":"Displacement (psychology)","level":2,"score":0.3716999888420105},{"id":"https://openalex.org/C61797465","wikidata":"https://www.wikidata.org/wiki/Q1188986","display_name":"Term (time)","level":2,"score":0.34279999136924744},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.3384000062942505},{"id":"https://openalex.org/C91306197","wikidata":"https://www.wikidata.org/wiki/Q45767","display_name":"Competition (biology)","level":2,"score":0.33230000734329224},{"id":"https://openalex.org/C178131030","wikidata":"https://www.wikidata.org/wiki/Q631360","display_name":"Price index","level":2,"score":0.32100000977516174},{"id":"https://openalex.org/C175444787","wikidata":"https://www.wikidata.org/wiki/Q39072","display_name":"Microeconomics","level":1,"score":0.3197000026702881},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3109999895095825},{"id":"https://openalex.org/C45473103","wikidata":"https://www.wikidata.org/wiki/Q851503","display_name":"Riccati equation","level":3,"score":0.3046000003814697},{"id":"https://openalex.org/C188466206","wikidata":"https://www.wikidata.org/wiki/Q7242626","display_name":"Price of stability","level":3,"score":0.30169999599456787},{"id":"https://openalex.org/C2777098679","wikidata":"https://www.wikidata.org/wiki/Q281682","display_name":"Imperfect competition","level":2,"score":0.29580000042915344},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.2946000099182129},{"id":"https://openalex.org/C48875124","wikidata":"https://www.wikidata.org/wiki/Q1416996","display_name":"Comparative statics","level":2,"score":0.29429998993873596},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.29429998993873596},{"id":"https://openalex.org/C103382277","wikidata":"https://www.wikidata.org/wiki/Q282640","display_name":"General equilibrium theory","level":2,"score":0.290800005197525},{"id":"https://openalex.org/C2780799671","wikidata":"https://www.wikidata.org/wiki/Q17087362","display_name":"Transient (computer programming)","level":2,"score":0.2858000099658966},{"id":"https://openalex.org/C70834904","wikidata":"https://www.wikidata.org/wiki/Q1054638","display_name":"Differential inclusion","level":2,"score":0.2793000042438507},{"id":"https://openalex.org/C73795354","wikidata":"https://www.wikidata.org/wiki/Q287618","display_name":"Sequential game","level":3,"score":0.2660999894142151},{"id":"https://openalex.org/C145912823","wikidata":"https://www.wikidata.org/wiki/Q113558","display_name":"Dynamics (music)","level":2,"score":0.2547000050544739}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.15901","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.15901","pdf_url":"https://arxiv.org/pdf/2609.15901","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":"doi:10.48550/arxiv.2609.15901","doi":"https://doi.org/10.48550/arxiv.2609.15901","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.15901","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2609.15901","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.15901","pdf_url":"https://arxiv.org/pdf/2609.15901","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":[],"study_designs":[],"awards":[{"id":"https://openalex.org/G4650965343","display_name":"Collaborative Research: CIF: Medium: Statistical and Algorithmic Foundations of Distributionally Robust Policy Learning","funder_award_id":"2312204","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G4931875759","display_name":"Collaborative Research: FET: Medium: Quantum Monte Carlo Speed Ups for Multilevel Computations and Other Statistical Algorithms","funder_award_id":"2403007","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G8876996369","display_name":null,"funder_award_id":"N00014","funder_id":"https://openalex.org/F4320337345","funder_display_name":"Office of Naval Research"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320337345","display_name":"Office of Naval Research","ror":"https://ror.org/00rk2pe57"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7213310225.pdf","grobid_xml":"https://content.openalex.org/works/W7213310225.grobid-xml"},"referenced_works_count":52,"referenced_works":["https://openalex.org/W1605834028","https://openalex.org/W1929167035","https://openalex.org/W2014256903","https://openalex.org/W2062122835","https://openalex.org/W2093362178","https://openalex.org/W2152947363","https://openalex.org/W2154016330","https://openalex.org/W2166944745","https://openalex.org/W2567583103","https://openalex.org/W2811434955","https://openalex.org/W2839502115","https://openalex.org/W2886768320","https://openalex.org/W2896164167","https://openalex.org/W2947566255","https://openalex.org/W2947587890","https://openalex.org/W2951194475","https://openalex.org/W2952841121","https://openalex.org/W2963791270","https://openalex.org/W2997414491","https://openalex.org/W3013600325","https://openalex.org/W3015272459","https://openalex.org/W3016303697","https://openalex.org/W3023274588","https://openalex.org/W3043568155","https://openalex.org/W3123018500","https://openalex.org/W3124021210","https://openalex.org/W3124367072","https://openalex.org/W3124692056","https://openalex.org/W3125048313","https://openalex.org/W3125789262","https://openalex.org/W3159360958","https://openalex.org/W3172945586","https://openalex.org/W3181839803","https://openalex.org/W3197842987","https://openalex.org/W4226027040","https://openalex.org/W4241749579","https://openalex.org/W4328129733","https://openalex.org/W4378718237","https://openalex.org/W4380352260","https://openalex.org/W4385952032","https://openalex.org/W4396820122","https://openalex.org/W4398190468","https://openalex.org/W4400715441","https://openalex.org/W4402596821","https://openalex.org/W4405680601","https://openalex.org/W4409150757","https://openalex.org/W4412082341","https://openalex.org/W4415100966","https://openalex.org/W7115598432","https://openalex.org/W7119779408","https://openalex.org/W7134193271","https://openalex.org/W7165527384"],"related_works":["https://openalex.org/W4226027040","https://openalex.org/W7062150143","https://openalex.org/W2896164167","https://openalex.org/W4365148600","https://openalex.org/W6889373573","https://openalex.org/W3123018500","https://openalex.org/W2040815543","https://openalex.org/W2782603341","https://openalex.org/W2540831527","https://openalex.org/W2781726695"],"abstract_inverted_index":{"We":[0],"study":[1],"a":[2,48,79,84,95,117],"continuous-time,":[3],"multiasset":[4],"trading":[5,143,166],"game":[6],"around":[7,138],"index":[8,20,45,74],"reconstitution,":[9],"in":[10],"which":[11],"opportunistic":[12,142],"traders":[13,34],"have":[14],"heterogeneous":[15],"beliefs":[16,41],"about":[17,42],"the":[18,43,55,62,68,72,145,156],"future":[19,44],"constitution":[21,46],"and":[22,29,58,100,105,120,124,140],"interact":[23],"through":[24],"transient":[25],"cross-asset":[26],"price":[27,136,150,175],"impact":[28],"instantaneous":[30],"execution":[31],"costs.":[32],"Opportunistic":[33],"build":[35],"inventory":[36],"based":[37],"on":[38],"their":[39,52],"individual":[40],"before":[47],"public":[49],"announcement,":[50],"adjust":[51],"positions":[53],"to":[54],"revealed":[56],"composition,":[57],"unwind":[59],"them":[60],"against":[61],"indexer's":[63,146],"prescribed":[64],"rebalancing":[65],"trades":[66],"at":[67],"implementation":[69,139,147],"date":[70],"when":[71],"new":[73],"composition":[75],"takes":[76],"effect.":[77],"Under":[78,112],"no-price-manipulation":[80],"condition,":[81],"we":[82,115],"construct":[83,116],"subgame-perfect":[85],"Nash":[86],"equilibrium.":[87],"Its":[88],"affine":[89],"feedback":[90],"policies":[91],"are":[92,107],"computed":[93],"from":[94],"non-standard":[96],"matrix":[97],"Riccati":[98],"equation":[99],"linear":[101],"ODEs":[102],"whose":[103],"number":[104],"dimensions":[106],"independent":[108],"of":[109],"population":[110],"size.":[111],"mean-field":[113,118],"scaling,":[114],"equilibrium":[119],"obtain":[121],"quantitative":[122],"convergence":[123],"approximate-Nash":[125],"bounds.":[126],"Numerical":[127],"illustrations":[128],"show":[129],"that":[130,141],"greater":[131,160],"competition":[132],"among":[133],"opportunists":[134],"dampens":[135],"swings":[137],"lowers":[144],"shortfall":[148],"unless":[149],"resilience":[151],"is":[152],"very":[153],"low.":[154],"Holding":[155],"average":[157],"belief":[158,161],"fixed,":[159],"dispersion":[162],"can":[163],"increase":[164],"gross":[165],"volume":[167],"without":[168],"changing":[169],"net":[170],"aggregate":[171],"opportunist":[172],"holdings":[173],"or":[174],"impact.":[176]},"counts_by_year":[],"updated_date":"2026-11-08T12:12:28.789561","created_date":"2026-09-16T00:00:00"}