{"id":"https://openalex.org/W2071981797","doi":"https://doi.org/10.1155/2013/285241","title":"Relationship between Maximum Principle and Dynamic Programming for Stochastic Recursive Optimal Control Problems and Applications","display_name":"Relationship between Maximum Principle and Dynamic Programming for Stochastic Recursive Optimal Control Problems and Applications","publication_year":2013,"publication_date":"2013-01-01","ids":{"openalex":"https://openalex.org/W2071981797","doi":"https://doi.org/10.1155/2013/285241","mag":"2071981797"},"language":"en","primary_location":{"id":"doi:10.1155/2013/285241","doi":"https://doi.org/10.1155/2013/285241","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2013/285241","pdf_url":"https://downloads.hindawi.com/journals/mpe/2013/285241.pdf","source":{"id":"https://openalex.org/S178238111","display_name":"Mathematical Problems in Engineering","issn_l":"1024-123X","issn":["1024-123X","1026-7077","1563-5147"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","cwts-core","poland-20","vabb-shw"],"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869","https://openalex.org/P4310320595"],"host_organization_lineage_names":["Hindawi Publishing Corporation","Wiley"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematical Problems in Engineering","raw_type":"journal-article"},"volume":null,"type":"article","is_traditional":true,"indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://downloads.hindawi.com/journals/mpe/2013/285241.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5075869928","display_name":"Jingtao Shi","orcid":"https://orcid.org/0000-0003-2736-6443","observed_orcids":["https://orcid.org/0000-0003-2736-6443"]},"institutions":[{"id":"https://openalex.org/I154099455","display_name":"Shandong University","ror":"https://ror.org/0207yh398","country_code":"CN","type":"education","lineage":["https://openalex.org/I154099455"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Jingtao Shi","raw_affiliation_strings":["School of Mathematics, Shandong University, Jinan 250100, China"],"raw_orcid":"https://orcid.org/0000-0003-2736-6443","affiliations":[{"raw_affiliation_string":"School of Mathematics, Shandong University, Jinan 250100, China","institution_ids":["https://openalex.org/I154099455"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5091067102","display_name":"Zhiyong Yu","orcid":"https://orcid.org/0000-0003-2343-7355","observed_orcids":["https://orcid.org/0000-0003-2343-7355","https://orcid.org/0009-0008-2403-0104"]},"institutions":[{"id":"https://openalex.org/I154099455","display_name":"Shandong University","ror":"https://ror.org/0207yh398","country_code":"CN","type":"education","lineage":["https://openalex.org/I154099455"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zhiyong Yu","raw_affiliation_strings":["School of Mathematics, Shandong University, Jinan 250100, China"],"raw_orcid":"https://orcid.org/0000-0003-2343-7355","affiliations":[{"raw_affiliation_string":"School of Mathematics, Shandong University, Jinan 250100, China","institution_ids":["https://openalex.org/I154099455"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5075869928"],"corresponding_institution_ids":["https://openalex.org/I154099455"],"apc_list":{"value":2550,"currency":"USD","value_usd":2550},"apc_paid":{"value":2550,"currency":"USD","value_usd":2550},"fwci":2.0309,"has_fulltext":true,"cited_by_count":16,"citation_normalized_percentile":{"value":0.88059465,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":87,"max":97},"biblio":{"volume":"2013","issue":null,"first_page":"1","last_page":"12"},"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/T10545","display_name":"Optimization and Variational Analysis","score":0.0008999999845400453,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12794","display_name":"Adaptive Dynamic Programming Control","score":0.0007999999797903001,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/maximum-principle","display_name":"maximum principle","score":0.8230000138282776},{"id":"https://openalex.org/keywords/dynamic-programming","display_name":"dynamic programming","score":0.9449999928474426},{"id":"https://openalex.org/keywords/adjoint-processes","display_name":"adjoint processes","score":0.9380000233650208},{"id":"https://openalex.org/keywords/value-function","display_name":"value function","score":0.9929999709129333},{"id":"https://openalex.org/keywords/recursive-utility","display_name":"recursive utility","score":0.7860000133514404},{"id":"https://openalex.org/keywords/portfolio-optimization","display_name":"portfolio optimization","score":0.9819999933242798},{"id":"https://openalex.org/keywords/linear-quadratic-control","display_name":"linear quadratic control","score":0.7419999837875366},{"id":"https://openalex.org/keywords/financial-engineering","display_name":"financial engineering","score":0.7289999723434448}],"concepts":[{"id":"https://openalex.org/C37404715","wikidata":"https://www.wikidata.org/wiki/Q380679","display_name":"Dynamic programming","level":2,"score":0.6562504768371582},{"id":"https://openalex.org/C14646407","wikidata":"https://www.wikidata.org/wiki/Q1430750","display_name":"Bellman equation","level":2,"score":0.6543945074081421},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.6474978923797607},{"id":"https://openalex.org/C202615002","wikidata":"https://www.wikidata.org/wiki/Q783507","display_name":"Differentiable function","level":2,"score":0.644162118434906},{"id":"https://openalex.org/C91575142","wikidata":"https://www.wikidata.org/wiki/Q1971426","display_name":"Optimal control","level":2,"score":0.6218172311782837},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6143051981925964},{"id":"https://openalex.org/C137631369","wikidata":"https://www.wikidata.org/wiki/Q7617831","display_name":"Stochastic programming","level":2,"score":0.5388644933700562},{"id":"https://openalex.org/C170131372","wikidata":"https://www.wikidata.org/wiki/Q7617811","display_name":"Stochastic control","level":3,"score":0.5275924801826477},{"id":"https://openalex.org/C31010330","wikidata":"https://www.wikidata.org/wiki/Q1914255","display_name":"Maximum principle","level":3,"score":0.5034939646720886},{"id":"https://openalex.org/C130787639","wikidata":"https://www.wikidata.org/wiki/Q5645293","display_name":"Hamiltonian (control theory)","level":2,"score":0.49865198135375977},{"id":"https://openalex.org/C2780821815","wikidata":"https://www.wikidata.org/wiki/Q5340806","display_name":"Portfolio","level":2,"score":0.4265189468860626},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3704564571380615},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.07411223649978638},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.06029835343360901},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.05996769666671753}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1155/2013/285241","doi":"https://doi.org/10.1155/2013/285241","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2013/285241","pdf_url":"https://downloads.hindawi.com/journals/mpe/2013/285241.pdf","source":{"id":"https://openalex.org/S178238111","display_name":"Mathematical Problems in Engineering","issn_l":"1024-123X","issn":["1024-123X","1026-7077","1563-5147"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","cwts-core","poland-20","vabb-shw"],"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869","https://openalex.org/P4310320595"],"host_organization_lineage_names":["Hindawi Publishing Corporation","Wiley"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematical Problems in Engineering","raw_type":"journal-article"},{"id":"pmh:oai:RePEc:hin:jnlmpe:285241","doi":null,"is_oa":false,"landing_page_url":"http://downloads.hindawi.com/journals/MPE/2013/285241.xml","pdf_url":null,"source":{"id":"https://openalex.org/S4306401271","display_name":"RePEc: Research Papers in Economics","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I77793887","host_organization_name":"Federal Reserve Bank of St. Louis","host_organization_lineage":["https://openalex.org/I77793887"],"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":"article"},{"id":"pmh:oai:doaj.org/article:4089727a1f924f2eaf696db4c9ef99fa","doi":null,"is_oa":true,"landing_page_url":"https://doaj.org/article/4089727a1f924f2eaf696db4c9ef99fa","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Mathematical Problems in Engineering, Vol 2013 (2013)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1155/2013/285241","doi":"https://doi.org/10.1155/2013/285241","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2013/285241","pdf_url":"https://downloads.hindawi.com/journals/mpe/2013/285241.pdf","source":{"id":"https://openalex.org/S178238111","display_name":"Mathematical Problems in Engineering","issn_l":"1024-123X","issn":["1024-123X","1026-7077","1563-5147"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","cwts-core","poland-20","vabb-shw"],"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869","https://openalex.org/P4310320595"],"host_organization_lineage_names":["Hindawi Publishing Corporation","Wiley"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematical Problems in Engineering","raw_type":"journal-article"},"sustainable_development_goals":[],"study_designs":[],"awards":[{"id":"https://openalex.org/G1112241806","display_name":null,"funder_award_id":"ZR2010AQ004","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G1652883609","display_name":null,"funder_award_id":"ZR2011AQ012","funder_id":"https://openalex.org/F4320338074","funder_display_name":"Government of Shandong Province"},{"id":"https://openalex.org/G1707304902","display_name":null,"funder_award_id":"11201264","funder_id":"https://openalex.org/F4320321543","funder_display_name":"China Postdoctoral Science Foundation"},{"id":"https://openalex.org/G2074372368","display_name":null,"funder_award_id":"ZR2010AQ004","funder_id":"https://openalex.org/F4320321543","funder_display_name":"China Postdoctoral Science Foundation"},{"id":"https://openalex.org/G518952628","display_name":null,"funder_award_id":"201002026","funder_id":"https://openalex.org/F4320321543","funder_display_name":"China Postdoctoral Science Foundation"},{"id":"https://openalex.org/G5317196203","display_name":null,"funder_award_id":"ZR2011AQ012","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G5400530374","display_name":null,"funder_award_id":"201002026","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G5649581576","display_name":null,"funder_award_id":"11101242","funder_id":"https://openalex.org/F4320321543","funder_display_name":"China Postdoctoral Science Foundation"},{"id":"https://openalex.org/G5668504162","display_name":null,"funder_award_id":"20100481278","funder_id":"https://openalex.org/F4320338074","funder_display_name":"Government of Shandong Province"},{"id":"https://openalex.org/G6674782250","display_name":null,"funder_award_id":"ZR2010AQ004","funder_id":"https://openalex.org/F4320338074","funder_display_name":"Government of Shandong Province"},{"id":"https://openalex.org/G7692589877","display_name":null,"funder_award_id":"20100481278","funder_id":"https://openalex.org/F4320321543","funder_display_name":"China Postdoctoral Science Foundation"},{"id":"https://openalex.org/G7696589302","display_name":null,"funder_award_id":"11101242","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G7841823022","display_name":null,"funder_award_id":"20100481278","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G7986129152","display_name":null,"funder_award_id":"11201264","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G8119370779","display_name":null,"funder_award_id":"201002026","funder_id":"https://openalex.org/F4320338074","funder_display_name":"Government of Shandong Province"},{"id":"https://openalex.org/G8816277420","display_name":null,"funder_award_id":"11101242","funder_id":"https://openalex.org/F4320338074","funder_display_name":"Government of Shandong Province"},{"id":"https://openalex.org/G8848587604","display_name":null,"funder_award_id":"ZR2011AQ012","funder_id":"https://openalex.org/F4320321543","funder_display_name":"China Postdoctoral Science Foundation"},{"id":"https://openalex.org/G893463933","display_name":null,"funder_award_id":"11201264","funder_id":"https://openalex.org/F4320338074","funder_display_name":"Government of Shandong Province"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320321543","display_name":"China Postdoctoral Science Foundation","ror":"https://ror.org/0426zh255"},{"id":"https://openalex.org/F4320338074","display_name":"Government of Shandong Province","ror":"https://ror.org/03jjt8440"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2071981797.pdf","grobid_xml":"https://content.openalex.org/works/W2071981797.grobid-xml"},"referenced_works_count":26,"referenced_works":["https://openalex.org/W1965542647","https://openalex.org/W1969717869","https://openalex.org/W1972204045","https://openalex.org/W1985059387","https://openalex.org/W1994823764","https://openalex.org/W1996900707","https://openalex.org/W2003293420","https://openalex.org/W2007734734","https://openalex.org/W2011192022","https://openalex.org/W2013627718","https://openalex.org/W2022173345","https://openalex.org/W2050593112","https://openalex.org/W2056551289","https://openalex.org/W2057567083","https://openalex.org/W2062925593","https://openalex.org/W2068168851","https://openalex.org/W2071533907","https://openalex.org/W2078895915","https://openalex.org/W2082734851","https://openalex.org/W2135400743","https://openalex.org/W2157883119","https://openalex.org/W2318557588","https://openalex.org/W3122650759","https://openalex.org/W3125895759","https://openalex.org/W4212780424","https://openalex.org/W4233775056"],"related_works":["https://openalex.org/W1481233145","https://openalex.org/W1570832990","https://openalex.org/W2106461302","https://openalex.org/W4416102408","https://openalex.org/W4402702047","https://openalex.org/W3112318516","https://openalex.org/W2119347091","https://openalex.org/W4404527863","https://openalex.org/W4321495841","https://openalex.org/W2296494068"],"abstract_inverted_index":{"This":[0],"paper":[1],"is":[2,50],"concerned":[3],"with":[4],"the":[5,25,28,33,47,58],"relationship":[6],"between":[7],"maximum":[8],"principle":[9],"and":[10,32],"dynamic":[11],"programming":[12],"for":[13],"stochastic":[14],"recursive":[15,41],"optimal":[16],"control":[17],"problems.":[18],"Under":[19],"certain":[20],"differentiability":[21],"conditions,":[22],"relations":[23],"among":[24],"adjoint":[26],"processes,":[27],"generalized":[29],"Hamiltonian":[30],"function,":[31],"value":[34],"function":[35],"are":[36],"given.":[37],"A":[38],"linear":[39],"quadratic":[40],"utility":[42],"portfolio":[43],"optimization":[44],"problem":[45],"in":[46],"financial":[48],"engineering":[49],"discussed":[51],"as":[52],"an":[53],"explicitly":[54],"illustrated":[55],"example":[56],"of":[57],"main":[59],"result.":[60]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2024,"cited_by_count":2},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":3}],"updated_date":"2026-11-08T12:12:28.789561","created_date":"2016-06-24T00:00:00"}