{"id":"https://openalex.org/W2019570835","doi":"https://doi.org/10.1137/110794845","title":"On the Hamilton--Jacobi--Bellman Equation for an Optimal Consumption Problem: I. Existence of Solution","display_name":"On the Hamilton--Jacobi--Bellman Equation for an Optimal Consumption Problem: I. Existence of Solution","publication_year":2012,"publication_date":"2012-01-01","ids":{"openalex":"https://openalex.org/W2019570835","doi":"https://doi.org/10.1137/110794845","mag":"2019570835"},"language":"en","primary_location":{"id":"doi:10.1137/110794845","is_oa":false,"landing_page_url":"https://doi.org/10.1137/110794845","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":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5007067467","display_name":"Hiroaki Hata","orcid":"https://orcid.org/0000-0001-8593-3501"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Hiroaki Hata","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5007752209","display_name":"Shuenn\u2010Jyi Sheu","orcid":"https://orcid.org/0000-0001-9605-5599"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Shuenn-Jyi Sheu","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5007067467"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":3.4603,"has_fulltext":false,"cited_by_count":28,"citation_normalized_percentile":{"value":0.93252721,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"50","issue":"4","first_page":"2373","last_page":"2400"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10067","display_name":"Stochastic processes and financial applications","score":0.9995999932289124,"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":0.9995999932289124,"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/T11413","display_name":"Risk and Portfolio Optimization","score":0.9939000010490417,"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"}},{"id":"https://openalex.org/T12137","display_name":"Economic theories and models","score":0.9778000116348267,"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/hamilton\u2013jacobi\u2013bellman-equation","display_name":"Hamilton\u2013Jacobi\u2013Bellman equation","score":0.9798358678817749},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7956154346466064},{"id":"https://openalex.org/keywords/uniqueness","display_name":"Uniqueness","score":0.7064323425292969},{"id":"https://openalex.org/keywords/bellman-equation","display_name":"Bellman equation","score":0.6681172847747803},{"id":"https://openalex.org/keywords/portfolio","display_name":"Portfolio","score":0.5608791708946228},{"id":"https://openalex.org/keywords/hamilton\u2013jacobi-equation","display_name":"Hamilton\u2013Jacobi equation","score":0.5582331418991089},{"id":"https://openalex.org/keywords/optimal-control","display_name":"Optimal control","score":0.46660324931144714},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.4570056200027466},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.44471243023872375},{"id":"https://openalex.org/keywords/mathematical-economics","display_name":"Mathematical economics","score":0.4249488413333893},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.19197452068328857},{"id":"https://openalex.org/keywords/economics","display_name":"Economics","score":0.10343307256698608}],"concepts":[{"id":"https://openalex.org/C196978813","wikidata":"https://www.wikidata.org/wiki/Q3302775","display_name":"Hamilton\u2013Jacobi\u2013Bellman equation","level":3,"score":0.9798358678817749},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7956154346466064},{"id":"https://openalex.org/C2777021972","wikidata":"https://www.wikidata.org/wiki/Q22976830","display_name":"Uniqueness","level":2,"score":0.7064323425292969},{"id":"https://openalex.org/C14646407","wikidata":"https://www.wikidata.org/wiki/Q1430750","display_name":"Bellman equation","level":2,"score":0.6681172847747803},{"id":"https://openalex.org/C2780821815","wikidata":"https://www.wikidata.org/wiki/Q5340806","display_name":"Portfolio","level":2,"score":0.5608791708946228},{"id":"https://openalex.org/C2778860007","wikidata":"https://www.wikidata.org/wiki/Q1060137","display_name":"Hamilton\u2013Jacobi equation","level":2,"score":0.5582331418991089},{"id":"https://openalex.org/C91575142","wikidata":"https://www.wikidata.org/wiki/Q1971426","display_name":"Optimal control","level":2,"score":0.46660324931144714},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4570056200027466},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.44471243023872375},{"id":"https://openalex.org/C144237770","wikidata":"https://www.wikidata.org/wiki/Q747534","display_name":"Mathematical economics","level":1,"score":0.4249488413333893},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.19197452068328857},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.10343307256698608},{"id":"https://openalex.org/C106159729","wikidata":"https://www.wikidata.org/wiki/Q2294553","display_name":"Financial economics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/110794845","is_oa":false,"landing_page_url":"https://doi.org/10.1137/110794845","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"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.4099999964237213,"id":"https://metadata.un.org/sdg/8","display_name":"Decent work and economic growth"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":27,"referenced_works":["https://openalex.org/W161655163","https://openalex.org/W1963901383","https://openalex.org/W1970973540","https://openalex.org/W1971750590","https://openalex.org/W1976860959","https://openalex.org/W1979878470","https://openalex.org/W1991552664","https://openalex.org/W2000196006","https://openalex.org/W2005158847","https://openalex.org/W2006776755","https://openalex.org/W2010317343","https://openalex.org/W2013530375","https://openalex.org/W2017588143","https://openalex.org/W2022729976","https://openalex.org/W2024495128","https://openalex.org/W2049388336","https://openalex.org/W2067390362","https://openalex.org/W2082304159","https://openalex.org/W2090220594","https://openalex.org/W2101295664","https://openalex.org/W2115292152","https://openalex.org/W2132264535","https://openalex.org/W2152557891","https://openalex.org/W2153579122","https://openalex.org/W2165176416","https://openalex.org/W3083001098","https://openalex.org/W3125981747"],"related_works":["https://openalex.org/W2032834442","https://openalex.org/W3153900688","https://openalex.org/W2115544975","https://openalex.org/W2902017027","https://openalex.org/W1654696814","https://openalex.org/W4291598237","https://openalex.org/W4239477580","https://openalex.org/W2766998270","https://openalex.org/W4226406511","https://openalex.org/W1996904445"],"abstract_inverted_index":{"We":[0,43],"consider":[1,91,112],"a":[2,39,65],"consumption":[3],"problem":[4,37],"with":[5],"an":[6,77,84],"infinite":[7],"time":[8],"horizon":[9],"to":[10],"optimize":[11],"the":[12,22,45,62,74,92,113,116,120],"discounted":[13],"expected":[14],"power":[15],"utility.":[16],"The":[17,36],"returns":[18],"and":[19,26,49,101,118],"volatilities":[20],"of":[21,64,76,80,87,115],"assets":[23],"are":[24],"random":[25],"affected":[27],"by":[28],"some":[29,57],"economic":[30],"factors,":[31],"modeled":[32],"as":[33],"diffusion":[34],"process.":[35],"becomes":[38],"standard":[40],"control":[41],"problem.":[42,96],"derive":[44],"Hamilton--Jacobi--Bellman":[46],"(HJB)":[47],"equation":[48,70],"study":[50],"its":[51],"solutions.":[52],"In":[53,97],"Part":[54,98],"I,":[55],"under":[56],"weak":[58],"conditions":[59],"we":[60,72,89,111],"prove":[61,119],"existence":[63,75],"solution":[66,117],"for":[67],"this":[68],"HJB":[69],"when":[71],"assume":[73],"ordered":[78,85],"pair":[79,86],"sub/supersolution.":[81],"To":[82],"construct":[83],"sub/supersolution,":[88],"also":[90],"risk-sensitive":[93],"portfolio":[94],"optimization":[95],"II":[99],"[Hata":[100],"Sheu,":[102],"SIAM":[103],"J.":[104],"Control":[105],"Optim.,":[106],"50":[107],"(2012),":[108],"pp.":[109],"2401--2430],":[110],"uniqueness":[114],"verification":[121],"theorem.":[122]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2023,"cited_by_count":3},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":5},{"year":2014,"cited_by_count":3},{"year":2012,"cited_by_count":1}],"updated_date":"2026-04-16T08:26:57.006410","created_date":"2025-10-10T00:00:00"}