{"id":"https://openalex.org/W1999201963","doi":"https://doi.org/10.1137/120897638","title":"A Weak Dynamic Programming Principle for Zero-Sum Stochastic Differential Games with Unbounded Controls","display_name":"A Weak Dynamic Programming Principle for Zero-Sum Stochastic Differential Games with Unbounded Controls","publication_year":2013,"publication_date":"2013-01-01","ids":{"openalex":"https://openalex.org/W1999201963","doi":"https://doi.org/10.1137/120897638","mag":"1999201963"},"language":"en","primary_location":{"id":"doi:10.1137/120897638","is_oa":false,"landing_page_url":"https://doi.org/10.1137/120897638","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":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1210.2788","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5005237318","display_name":"Erhan Bayraktar","orcid":"https://orcid.org/0000-0002-1926-4570"},"institutions":[{"id":"https://openalex.org/I27837315","display_name":"University of Michigan\u2013Ann Arbor","ror":"https://ror.org/00jmfr291","country_code":"US","type":"education","lineage":["https://openalex.org/I27837315"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Erhan Bayraktar","raw_affiliation_strings":["University of Michigan at Ann Arbor - Department of Mathematics"],"affiliations":[{"raw_affiliation_string":"University of Michigan at Ann Arbor - Department of Mathematics","institution_ids":["https://openalex.org/I27837315"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5038103852","display_name":"Song Yao","orcid":"https://orcid.org/0000-0001-7046-9873"},"institutions":[{"id":"https://openalex.org/I170201317","display_name":"University of Pittsburgh","ror":"https://ror.org/01an3r305","country_code":"US","type":"education","lineage":["https://openalex.org/I170201317"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Song Yao","raw_affiliation_strings":["University of Pittsburgh"],"affiliations":[{"raw_affiliation_string":"University of Pittsburgh","institution_ids":["https://openalex.org/I170201317"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5005237318"],"corresponding_institution_ids":["https://openalex.org/I27837315"],"apc_list":null,"apc_paid":null,"fwci":0.4311,"has_fulltext":true,"cited_by_count":2,"citation_normalized_percentile":{"value":0.71367017,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"51","issue":"3","first_page":"2036","last_page":"2080"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10067","display_name":"Stochastic processes and financial applications","score":0.9994000196456909,"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":0.9994000196456909,"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":0.9954000115394592,"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/T12011","display_name":"Insurance, Mortality, Demography, Risk Management","score":0.984499990940094,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/differential-game","display_name":"Differential game","score":0.7522764205932617},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6863349676132202},{"id":"https://openalex.org/keywords/zero","display_name":"Zero (linguistics)","score":0.6379674673080444},{"id":"https://openalex.org/keywords/zero-sum-game","display_name":"Zero-sum game","score":0.5957335233688354},{"id":"https://openalex.org/keywords/dynamic-programming","display_name":"Dynamic programming","score":0.577528178691864},{"id":"https://openalex.org/keywords/viscosity-solution","display_name":"Viscosity solution","score":0.5228505730628967},{"id":"https://openalex.org/keywords/differential","display_name":"Differential (mechanical device)","score":0.5100151300430298},{"id":"https://openalex.org/keywords/example-of-a-game-without-a-value","display_name":"Example of a game without a value","score":0.5059449076652527},{"id":"https://openalex.org/keywords/stochastic-differential-equation","display_name":"Stochastic differential equation","score":0.46809127926826477},{"id":"https://openalex.org/keywords/bellman-equation","display_name":"Bellman equation","score":0.4243204593658447},{"id":"https://openalex.org/keywords/sequential-game","display_name":"Sequential game","score":0.40645307302474976},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4051395654678345},{"id":"https://openalex.org/keywords/mathematical-economics","display_name":"Mathematical economics","score":0.3875705897808075},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3005324602127075},{"id":"https://openalex.org/keywords/game-theory","display_name":"Game theory","score":0.24047347903251648},{"id":"https://openalex.org/keywords/combinatorial-game-theory","display_name":"Combinatorial game theory","score":0.16521629691123962},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.0898408591747284}],"concepts":[{"id":"https://openalex.org/C2779006483","wikidata":"https://www.wikidata.org/wiki/Q1973196","display_name":"Differential game","level":2,"score":0.7522764205932617},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6863349676132202},{"id":"https://openalex.org/C2780813799","wikidata":"https://www.wikidata.org/wiki/Q3274237","display_name":"Zero (linguistics)","level":2,"score":0.6379674673080444},{"id":"https://openalex.org/C136356330","wikidata":"https://www.wikidata.org/wiki/Q156612","display_name":"Zero-sum game","level":3,"score":0.5957335233688354},{"id":"https://openalex.org/C37404715","wikidata":"https://www.wikidata.org/wiki/Q380679","display_name":"Dynamic programming","level":2,"score":0.577528178691864},{"id":"https://openalex.org/C88731125","wikidata":"https://www.wikidata.org/wiki/Q7935676","display_name":"Viscosity solution","level":2,"score":0.5228505730628967},{"id":"https://openalex.org/C93226319","wikidata":"https://www.wikidata.org/wiki/Q193137","display_name":"Differential (mechanical device)","level":2,"score":0.5100151300430298},{"id":"https://openalex.org/C138328387","wikidata":"https://www.wikidata.org/wiki/Q5419308","display_name":"Example of a game without a value","level":5,"score":0.5059449076652527},{"id":"https://openalex.org/C51955184","wikidata":"https://www.wikidata.org/wiki/Q1545585","display_name":"Stochastic differential equation","level":2,"score":0.46809127926826477},{"id":"https://openalex.org/C14646407","wikidata":"https://www.wikidata.org/wiki/Q1430750","display_name":"Bellman equation","level":2,"score":0.4243204593658447},{"id":"https://openalex.org/C73795354","wikidata":"https://www.wikidata.org/wiki/Q287618","display_name":"Sequential game","level":3,"score":0.40645307302474976},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4051395654678345},{"id":"https://openalex.org/C144237770","wikidata":"https://www.wikidata.org/wiki/Q747534","display_name":"Mathematical economics","level":1,"score":0.3875705897808075},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3005324602127075},{"id":"https://openalex.org/C177142836","wikidata":"https://www.wikidata.org/wiki/Q44455","display_name":"Game theory","level":2,"score":0.24047347903251648},{"id":"https://openalex.org/C102234262","wikidata":"https://www.wikidata.org/wiki/Q1320931","display_name":"Combinatorial game theory","level":4,"score":0.16521629691123962},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0898408591747284},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0}],"mesh":[],"locations_count":6,"locations":[{"id":"doi:10.1137/120897638","is_oa":false,"landing_page_url":"https://doi.org/10.1137/120897638","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:arXiv.org:1210.2788","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1210.2788","pdf_url":"https://arxiv.org/pdf/1210.2788","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":"mag:2952896596","is_oa":true,"landing_page_url":"http://export.arxiv.org/pdf/1210.2788","pdf_url":null,"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":"arXiv (Cornell University)","raw_type":null},{"id":"mag:1999201963","is_oa":true,"landing_page_url":"https://papers.ssrn.com/sol3/Delivery.cfm/SSRN_ID2807541_code2193409.pdf?abstractid=2395451&mirid=2","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,"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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"SSRN Electronic Journal","raw_type":null},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.762.9912","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.762.9912","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://arxiv.org/pdf/1210.2788.pdf","raw_type":"text"},{"id":"doi:10.48550/arxiv.1210.2788","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1210.2788","pdf_url":null,"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":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1210.2788","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1210.2788","pdf_url":"https://arxiv.org/pdf/1210.2788","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":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1999201963.pdf","grobid_xml":"https://content.openalex.org/works/W1999201963.grobid-xml"},"referenced_works_count":30,"referenced_works":["https://openalex.org/W649943522","https://openalex.org/W1580561995","https://openalex.org/W1971594473","https://openalex.org/W1982083851","https://openalex.org/W1985296147","https://openalex.org/W1998407679","https://openalex.org/W2005040225","https://openalex.org/W2007734734","https://openalex.org/W2007849171","https://openalex.org/W2017032949","https://openalex.org/W2022558670","https://openalex.org/W2022944519","https://openalex.org/W2045577524","https://openalex.org/W2046047743","https://openalex.org/W2066590618","https://openalex.org/W2078895915","https://openalex.org/W2083184780","https://openalex.org/W2115847660","https://openalex.org/W2138897654","https://openalex.org/W2154825028","https://openalex.org/W2157883119","https://openalex.org/W2963113471","https://openalex.org/W3037779091","https://openalex.org/W3100306062","https://openalex.org/W3103126577","https://openalex.org/W3121250812","https://openalex.org/W3121898758","https://openalex.org/W3123347787","https://openalex.org/W3125153217","https://openalex.org/W4243590097"],"related_works":["https://openalex.org/W3123934717","https://openalex.org/W2135438301","https://openalex.org/W3168961250","https://openalex.org/W1484721121","https://openalex.org/W2024639455","https://openalex.org/W2035752095","https://openalex.org/W3105327397","https://openalex.org/W1515928315","https://openalex.org/W3032373464","https://openalex.org/W2002165199","https://openalex.org/W1956626475","https://openalex.org/W2962927879","https://openalex.org/W2962982619","https://openalex.org/W2046047743","https://openalex.org/W2947657784","https://openalex.org/W2136227587","https://openalex.org/W1556399212","https://openalex.org/W3105644870","https://openalex.org/W1996616837","https://openalex.org/W3208728045"],"abstract_inverted_index":{"We":[0,28],"analyze":[1],"a":[2,36],"zero-sum":[3],"stochastic":[4,25],"differential":[5,26,49],"game":[6,20],"between":[7],"two":[8],"competing":[9],"players":[10],"who":[11],"can":[12],"choose":[13],"unbounded":[14],"controls.":[15],"The":[16],"payoffs":[17],"of":[18],"the":[19,44,52],"are":[21],"defined":[22],"through":[23],"backward":[24],"equations.":[27],"prove":[29],"that":[30],"each":[31],"player's":[32],"priority":[33],"value":[34],"satisfies":[35],"weak":[37],"dynamic":[38],"programming":[39],"principle":[40],"and":[41],"thus":[42],"solves":[43],"associated":[45],"fully":[46],"nonlinear":[47],"partial":[48],"equation":[50],"in":[51],"viscosity":[53],"sense.":[54]},"counts_by_year":[{"year":2017,"cited_by_count":1},{"year":2014,"cited_by_count":1}],"updated_date":"2026-03-10T16:38:18.471706","created_date":"2025-10-10T00:00:00"}
