{"id":"https://openalex.org/W2024495128","doi":"https://doi.org/10.1137/110794857","title":"On the Hamilton--Jacobi--Bellman Equation for an Optimal Consumption Problem: II. Verification Theorem","display_name":"On the Hamilton--Jacobi--Bellman Equation for an Optimal Consumption Problem: II. Verification Theorem","publication_year":2012,"publication_date":"2012-01-01","ids":{"openalex":"https://openalex.org/W2024495128","doi":"https://doi.org/10.1137/110794857","mag":"2024495128"},"language":"en","primary_location":{"id":"doi:10.1137/110794857","is_oa":false,"landing_page_url":"https://doi.org/10.1137/110794857","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":2.2305,"has_fulltext":false,"cited_by_count":18,"citation_normalized_percentile":{"value":0.89612453,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"50","issue":"4","first_page":"2401","last_page":"2430"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10067","display_name":"Stochastic processes and financial applications","score":0.9965999722480774,"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":0.9965999722480774,"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":0.9914000034332275,"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/T11413","display_name":"Risk and Portfolio Optimization","score":0.9851999878883362,"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/hamilton\u2013jacobi\u2013bellman-equation","display_name":"Hamilton\u2013Jacobi\u2013Bellman equation","score":0.9934709072113037},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8083122968673706},{"id":"https://openalex.org/keywords/dynamic-programming","display_name":"Dynamic programming","score":0.6194595694541931},{"id":"https://openalex.org/keywords/viscosity-solution","display_name":"Viscosity solution","score":0.5159440636634827},{"id":"https://openalex.org/keywords/bellman-equation","display_name":"Bellman equation","score":0.5116965770721436},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.48341262340545654},{"id":"https://openalex.org/keywords/stochastic-differential-equation","display_name":"Stochastic differential equation","score":0.47931066155433655},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.46791890263557434},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.4432949125766754},{"id":"https://openalex.org/keywords/mathematical-economics","display_name":"Mathematical economics","score":0.3833678066730499},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.24942564964294434}],"concepts":[{"id":"https://openalex.org/C196978813","wikidata":"https://www.wikidata.org/wiki/Q3302775","display_name":"Hamilton\u2013Jacobi\u2013Bellman equation","level":3,"score":0.9934709072113037},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8083122968673706},{"id":"https://openalex.org/C37404715","wikidata":"https://www.wikidata.org/wiki/Q380679","display_name":"Dynamic programming","level":2,"score":0.6194595694541931},{"id":"https://openalex.org/C88731125","wikidata":"https://www.wikidata.org/wiki/Q7935676","display_name":"Viscosity solution","level":2,"score":0.5159440636634827},{"id":"https://openalex.org/C14646407","wikidata":"https://www.wikidata.org/wiki/Q1430750","display_name":"Bellman equation","level":2,"score":0.5116965770721436},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.48341262340545654},{"id":"https://openalex.org/C51955184","wikidata":"https://www.wikidata.org/wiki/Q1545585","display_name":"Stochastic differential equation","level":2,"score":0.47931066155433655},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.46791890263557434},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.4432949125766754},{"id":"https://openalex.org/C144237770","wikidata":"https://www.wikidata.org/wiki/Q747534","display_name":"Mathematical economics","level":1,"score":0.3833678066730499},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.24942564964294434}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/110794857","is_oa":false,"landing_page_url":"https://doi.org/10.1137/110794857","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":[{"display_name":"Decent work and economic growth","score":0.41999998688697815,"id":"https://metadata.un.org/sdg/8"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":10,"referenced_works":["https://openalex.org/W1976860959","https://openalex.org/W2000196006","https://openalex.org/W2010317343","https://openalex.org/W2019570835","https://openalex.org/W2022996397","https://openalex.org/W2049388336","https://openalex.org/W2115292152","https://openalex.org/W2121355865","https://openalex.org/W2165176416","https://openalex.org/W3102856490"],"related_works":["https://openalex.org/W4239477580","https://openalex.org/W4255265352","https://openalex.org/W2032834442","https://openalex.org/W1654696814","https://openalex.org/W3153900688","https://openalex.org/W2921905705","https://openalex.org/W4297940580","https://openalex.org/W4306892756","https://openalex.org/W2766998270","https://openalex.org/W1632524629"],"abstract_inverted_index":{"We":[0,24,108],"consider":[1,88],"an":[2,7],"optimal":[3,96],"consumption":[4],"problem":[5],"where":[6],"investor":[8],"tries":[9],"to":[10],"maximize":[11],"the":[12,32,45,59,72,89,110,131],"infinite":[13],"horizon":[14],"expected":[15],"discounted":[16],"hyperbolic":[17],"absolute":[18],"risk":[19],"aversion":[20],"utility":[21],"of":[22,35,47,74,95,102,115],"consumption.":[23],"treat":[25],"a":[26,48,53,75,93,100,119,125],"stochastic":[27,49],"factor":[28],"model":[29],"such":[30],"that":[31],"mean":[33],"returns":[34],"risky":[36],"assets":[37],"depend":[38],"on":[39],"underlying":[40],"economic":[41],"factors":[42],"formulated":[43],"as":[44],"solution":[46,77,101],"differential":[50],"equation.":[51],"Using":[52],"dynamic":[54],"programming":[55],"principle,":[56],"we":[57,70,87],"derive":[58],"Hamilton--Jacobi--Bellman":[60],"(HJB)":[61],"equation":[62,80,104],"and":[63,122],"study":[64],"its":[65],"solutions.":[66,138],"In":[67,84,128],"part":[68,85],"I,":[69],"prove":[71,109],"existence":[73],"classical":[76],"for":[78],"HJB":[79,103,132],"under":[81,112],"suitable":[82],"conditions.":[83,116],"II,":[86],"verification":[90],"theorem":[91],"stating":[92],"candidate":[94],"strategy":[97],"derived":[98],"from":[99],"is":[105,118,124],"indeed":[106],"optimal.":[107],"result":[111],"two":[113],"sets":[114],"One":[117],"linear":[120],"model,":[121],"one":[123],"nonlinear":[126],"model.":[127],"both":[129],"cases,":[130],"equations":[133],"do":[134],"not":[135],"have":[136],"analytical":[137]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2023,"cited_by_count":2},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":2},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":3},{"year":2012,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}