{"id":"https://openalex.org/W2161582152","doi":"https://doi.org/10.1137/080730354","title":"Stochastic Equations with Delay: Optimal Control via BSDEs and Regular Solutions of Hamilton\u2013Jacobi\u2013Bellman Equations","display_name":"Stochastic Equations with Delay: Optimal Control via BSDEs and Regular Solutions of Hamilton\u2013Jacobi\u2013Bellman Equations","publication_year":2010,"publication_date":"2010-01-01","ids":{"openalex":"https://openalex.org/W2161582152","doi":"https://doi.org/10.1137/080730354","mag":"2161582152"},"language":"en","primary_location":{"id":"doi:10.1137/080730354","is_oa":false,"landing_page_url":"https://doi.org/10.1137/080730354","pdf_url":null,"source":{"id":"https://openalex.org/S897311980","display_name":"SIAM Journal on Control and Optimization","issn_l":"0363-0129","issn":["0363-0129","1095-7138"],"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 Control and Optimization","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"http://hdl.handle.net/2434/661790","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5004737909","display_name":"Marco Fuhrman","orcid":"https://orcid.org/0000-0002-9325-7053"},"institutions":[{"id":"https://openalex.org/I93860229","display_name":"Politecnico di Milano","ror":"https://ror.org/01nffqt88","country_code":"IT","type":"education","lineage":["https://openalex.org/I93860229"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Marco Fuhrman","raw_affiliation_strings":["Politecnico di Milano, Dipartimento di Matematica, piazza Leonardo da Vinci 32, 20133 Milano, Italy"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Politecnico di Milano, Dipartimento di Matematica, piazza Leonardo da Vinci 32, 20133 Milano, Italy","institution_ids":["https://openalex.org/I93860229"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5061651419","display_name":"Federica Masiero","orcid":"https://orcid.org/0000-0002-6761-0837"},"institutions":[{"id":"https://openalex.org/I66752286","display_name":"University of Milano-Bicocca","ror":"https://ror.org/01ynf4891","country_code":"IT","type":"education","lineage":["https://openalex.org/I66752286"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Federica Masiero","raw_affiliation_strings":["Dipartimento di Matematica e Applicazioni, Universit\u00e0 di Milano Bicocca, via Cozzi 53, 20125 Milano, Italy"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Dipartimento di Matematica e Applicazioni, Universit\u00e0 di Milano Bicocca, via Cozzi 53, 20125 Milano, Italy","institution_ids":["https://openalex.org/I66752286"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5041696665","display_name":"Gianmario Tessitore","orcid":"https://orcid.org/0000-0001-9893-3703"},"institutions":[{"id":"https://openalex.org/I66752286","display_name":"University of Milano-Bicocca","ror":"https://ror.org/01ynf4891","country_code":"IT","type":"education","lineage":["https://openalex.org/I66752286"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Gianmario Tessitore","raw_affiliation_strings":["Dipartimento di Matematica e Applicazioni, Universit\u00e0 di Milano Bicocca, via Cozzi 53, 20125 Milano, Italy"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Dipartimento di Matematica e Applicazioni, Universit\u00e0 di Milano Bicocca, via Cozzi 53, 20125 Milano, Italy","institution_ids":["https://openalex.org/I66752286"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":3.4575,"has_fulltext":false,"cited_by_count":61,"citation_normalized_percentile":{"value":0.93099283,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"48","issue":"7","first_page":"4624","last_page":"4651"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10067","display_name":"Stochastic processes and financial applications","score":0.9997000098228455,"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":0.9997000098228455,"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/T12011","display_name":"Insurance, Mortality, Demography, Risk Management","score":0.980400025844574,"subfield":{"id":"https://openalex.org/subfields/3317","display_name":"Demography"},"field":{"id":"https://openalex.org/fields/33","display_name":"Social Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T10282","display_name":"Financial Risk and Volatility Modeling","score":0.9605000019073486,"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/mathematics","display_name":"Mathematics","score":0.7953536510467529},{"id":"https://openalex.org/keywords/stochastic-differential-equation","display_name":"Stochastic differential equation","score":0.7535854578018188},{"id":"https://openalex.org/keywords/brownian-motion","display_name":"Brownian motion","score":0.624934196472168},{"id":"https://openalex.org/keywords/generator","display_name":"Generator (circuit theory)","score":0.5822969079017639},{"id":"https://openalex.org/keywords/space","display_name":"Space (punctuation)","score":0.4835371971130371},{"id":"https://openalex.org/keywords/optimal-control","display_name":"Optimal control","score":0.45835983753204346},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.45799097418785095},{"id":"https://openalex.org/keywords/geometric-brownian-motion","display_name":"Geometric Brownian motion","score":0.4525153636932373},{"id":"https://openalex.org/keywords/hamilton\u2013jacobi-equation","display_name":"Hamilton\u2013Jacobi equation","score":0.4475541412830353},{"id":"https://openalex.org/keywords/stochastic-partial-differential-equation","display_name":"Stochastic partial differential equation","score":0.4427134394645691},{"id":"https://openalex.org/keywords/stochastic-control","display_name":"Stochastic control","score":0.4374120831489563},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4187593460083008},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.4128759503364563},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3804408311843872},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.2308838963508606},{"id":"https://openalex.org/keywords/diffusion-process","display_name":"Diffusion process","score":0.21743813157081604},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.10185441374778748}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7953536510467529},{"id":"https://openalex.org/C51955184","wikidata":"https://www.wikidata.org/wiki/Q1545585","display_name":"Stochastic differential equation","level":2,"score":0.7535854578018188},{"id":"https://openalex.org/C112401455","wikidata":"https://www.wikidata.org/wiki/Q178036","display_name":"Brownian motion","level":2,"score":0.624934196472168},{"id":"https://openalex.org/C2780992000","wikidata":"https://www.wikidata.org/wiki/Q17016113","display_name":"Generator (circuit theory)","level":3,"score":0.5822969079017639},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.4835371971130371},{"id":"https://openalex.org/C91575142","wikidata":"https://www.wikidata.org/wiki/Q1971426","display_name":"Optimal control","level":2,"score":0.45835983753204346},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.45799097418785095},{"id":"https://openalex.org/C101615488","wikidata":"https://www.wikidata.org/wiki/Q1503307","display_name":"Geometric Brownian motion","level":4,"score":0.4525153636932373},{"id":"https://openalex.org/C2778860007","wikidata":"https://www.wikidata.org/wiki/Q1060137","display_name":"Hamilton\u2013Jacobi equation","level":2,"score":0.4475541412830353},{"id":"https://openalex.org/C84629840","wikidata":"https://www.wikidata.org/wiki/Q16979017","display_name":"Stochastic partial differential equation","level":3,"score":0.4427134394645691},{"id":"https://openalex.org/C170131372","wikidata":"https://www.wikidata.org/wiki/Q7617811","display_name":"Stochastic control","level":3,"score":0.4374120831489563},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4187593460083008},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.4128759503364563},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3804408311843872},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.2308838963508606},{"id":"https://openalex.org/C68710425","wikidata":"https://www.wikidata.org/wiki/Q5275442","display_name":"Diffusion process","level":3,"score":0.21743813157081604},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.10185441374778748},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0},{"id":"https://openalex.org/C3017618536","wikidata":"https://www.wikidata.org/wiki/Q304994","display_name":"Innovation diffusion","level":2,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C56739046","wikidata":"https://www.wikidata.org/wiki/Q192060","display_name":"Knowledge management","level":1,"score":0.0},{"id":"https://openalex.org/C163258240","wikidata":"https://www.wikidata.org/wiki/Q25342","display_name":"Power (physics)","level":2,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1137/080730354","is_oa":false,"landing_page_url":"https://doi.org/10.1137/080730354","pdf_url":null,"source":{"id":"https://openalex.org/S897311980","display_name":"SIAM Journal on Control and Optimization","issn_l":"0363-0129","issn":["0363-0129","1095-7138"],"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 Control and Optimization","raw_type":"journal-article"},{"id":"pmh:oai:air.unimi.it:2434/661790","is_oa":true,"landing_page_url":"http://hdl.handle.net/2434/661790","pdf_url":null,"source":{"id":"https://openalex.org/S4306400516","display_name":"Archivio Istituzionale della Ricerca (Universita Degli Studi Di Milano)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I189158943","host_organization_name":"University of Milan","host_organization_lineage":["https://openalex.org/I189158943"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:boa.unimib.it:10281/20936","is_oa":false,"landing_page_url":"http://hdl.handle.net/10281/20936","pdf_url":null,"source":{"id":"https://openalex.org/S4306401259","display_name":"BOA (University of Milano-Bicocca)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I66752286","host_organization_name":"University of Milano-Bicocca","host_organization_lineage":["https://openalex.org/I66752286"],"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":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"pmh:oai:air.unimi.it:2434/661790","is_oa":true,"landing_page_url":"http://hdl.handle.net/2434/661790","pdf_url":null,"source":{"id":"https://openalex.org/S4306400516","display_name":"Archivio Istituzionale della Ricerca (Universita Degli Studi Di Milano)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I189158943","host_organization_name":"University of Milan","host_organization_lineage":["https://openalex.org/I189158943"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"info:eu-repo/semantics/article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":27,"referenced_works":["https://openalex.org/W564397617","https://openalex.org/W639984306","https://openalex.org/W1482876438","https://openalex.org/W1489605740","https://openalex.org/W1505057802","https://openalex.org/W1530927473","https://openalex.org/W1542004730","https://openalex.org/W1554577510","https://openalex.org/W1558902221","https://openalex.org/W1985170541","https://openalex.org/W1986974679","https://openalex.org/W1992472513","https://openalex.org/W1994791309","https://openalex.org/W2009602427","https://openalex.org/W2019054284","https://openalex.org/W2022273243","https://openalex.org/W2028341348","https://openalex.org/W2034413077","https://openalex.org/W2037175628","https://openalex.org/W2050294302","https://openalex.org/W2057612205","https://openalex.org/W2066157328","https://openalex.org/W2078895915","https://openalex.org/W2079871064","https://openalex.org/W2157883119","https://openalex.org/W2171586580","https://openalex.org/W2576386146"],"related_works":["https://openalex.org/W620239920","https://openalex.org/W2015493381","https://openalex.org/W2949279289","https://openalex.org/W109055908","https://openalex.org/W2797751308","https://openalex.org/W1546584948","https://openalex.org/W2060658157","https://openalex.org/W2972896374","https://openalex.org/W4237379163","https://openalex.org/W2745153931"],"abstract_inverted_index":{"We":[0,36,72,122],"consider":[1,38],"an":[2,16],"It\u00f4":[3],"stochastic":[4,41,128],"differential":[5,42,89,131],"equation":[6,43,132],"with":[7,24,33,47,119,133],"delay,":[8],"driven":[9,95],"by":[10,15,96],"Brownian":[11],"motion,":[12],"whose":[13],"solution,":[14],"appropriate":[17],"reformulation,":[18],"defines":[19],"a":[20,27,39,67,80,84,105,116],"Markov":[21],"process":[22,64,148],"X":[23],"values":[25],"in":[26,59,135,144],"space":[28,93],"of":[29,55,70,86,107,130,146],"continuous":[30],"functions":[31],"$\\mathbf{C}$,":[32],"generator":[34],"$\\mathcal{L}$.":[35],"then":[37],"backward":[40],"depending":[44],"on":[45,91],"X,":[46],"unknown":[48],"processes":[49],"$(Y,Z)$,":[50],"and":[51,98,111],"we":[52,61,99,137],"study":[53],"properties":[54],"the":[56,63,76,92,108,112,147],"resulting":[57],"system,":[58],"particular":[60,136],"identify":[62],"Z":[65],"as":[66,141],"deterministic":[68],"functional":[69],"X.":[71,149],"next":[73],"prove":[74,104],"that":[75],"forward-backward":[77],"system":[78],"provides":[79],"suitable":[81],"solution":[82],"to":[83,103,126],"class":[85],"parabolic":[87],"partial":[88],"equations":[90],"$\\mathbf{C}$":[94],"$\\mathcal{L}$,":[97],"apply":[100],"this":[101],"result":[102],"characterization":[106],"fair":[109],"price":[110],"hedging":[113],"strategy":[114],"for":[115],"financial":[117],"market":[118],"memory":[120],"effects.":[121],"also":[123],"include":[124],"applications":[125],"optimal":[127,139],"control":[129],"delay:":[134],"characterize":[138],"controls":[140],"feedback":[142],"laws":[143],"terms":[145]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":4},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":7},{"year":2020,"cited_by_count":6},{"year":2019,"cited_by_count":5},{"year":2018,"cited_by_count":6},{"year":2017,"cited_by_count":4},{"year":2016,"cited_by_count":7},{"year":2015,"cited_by_count":4},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":4}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
