{"id":"https://openalex.org/W2887893637","doi":"https://doi.org/10.1137/19m1245049","title":"Optimal Control of Debt-to-GDP Ratio in an $N$-State Regime Switching Economy","display_name":"Optimal Control of Debt-to-GDP Ratio in an $N$-State Regime Switching Economy","publication_year":2020,"publication_date":"2020-01-01","ids":{"openalex":"https://openalex.org/W2887893637","doi":"https://doi.org/10.1137/19m1245049","mag":"2887893637"},"language":"en","primary_location":{"id":"doi:10.1137/19m1245049","is_oa":false,"landing_page_url":"https://doi.org/10.1137/19m1245049","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":"preprint","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1808.01499","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5020814759","display_name":"Giorgio Ferrari","orcid":"https://orcid.org/0000-0002-2125-3301"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Giorgio Ferrari","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5065206582","display_name":"N\u00e9ofytos Rodosthenous","orcid":"https://orcid.org/0000-0003-3614-2206"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Neofytos Rodosthenous","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5020814759"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.00712168,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"58","issue":"2","first_page":"755","last_page":"786"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10067","display_name":"Stochastic processes and financial applications","score":0.9860000014305115,"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":0.9860000014305115,"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/T10007","display_name":"Monetary Policy and Economic Impact","score":0.9851999878883362,"subfield":{"id":"https://openalex.org/subfields/2000","display_name":"General Economics, Econometrics and 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/T10471","display_name":"Climate Change Policy and Economics","score":0.9740999937057495,"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/debt","display_name":"Debt","score":0.5569797158241272},{"id":"https://openalex.org/keywords/economics","display_name":"Economics","score":0.5337048172950745},{"id":"https://openalex.org/keywords/interval","display_name":"Interval (graph theory)","score":0.4826377034187317},{"id":"https://openalex.org/keywords/debt-ratio","display_name":"Debt ratio","score":0.4738008379936218},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.4640589952468872},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3509503901004791},{"id":"https://openalex.org/keywords/monetary-economics","display_name":"Monetary economics","score":0.35007283091545105},{"id":"https://openalex.org/keywords/economy","display_name":"Economy","score":0.3435057997703552},{"id":"https://openalex.org/keywords/econometrics","display_name":"Econometrics","score":0.3426443338394165},{"id":"https://openalex.org/keywords/finance","display_name":"Finance","score":0.2288927435874939}],"concepts":[{"id":"https://openalex.org/C120527767","wikidata":"https://www.wikidata.org/wiki/Q3196867","display_name":"Debt","level":2,"score":0.5569797158241272},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.5337048172950745},{"id":"https://openalex.org/C2778067643","wikidata":"https://www.wikidata.org/wiki/Q166507","display_name":"Interval (graph theory)","level":2,"score":0.4826377034187317},{"id":"https://openalex.org/C135665773","wikidata":"https://www.wikidata.org/wiki/Q2234049","display_name":"Debt ratio","level":3,"score":0.4738008379936218},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.4640589952468872},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3509503901004791},{"id":"https://openalex.org/C556758197","wikidata":"https://www.wikidata.org/wiki/Q580018","display_name":"Monetary economics","level":1,"score":0.35007283091545105},{"id":"https://openalex.org/C136264566","wikidata":"https://www.wikidata.org/wiki/Q159810","display_name":"Economy","level":1,"score":0.3435057997703552},{"id":"https://openalex.org/C149782125","wikidata":"https://www.wikidata.org/wiki/Q160039","display_name":"Econometrics","level":1,"score":0.3426443338394165},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.2288927435874939},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.0}],"mesh":[],"locations_count":8,"locations":[{"id":"doi:10.1137/19m1245049","is_oa":false,"landing_page_url":"https://doi.org/10.1137/19m1245049","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:1808.01499","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1808.01499","pdf_url":"https://arxiv.org/pdf/1808.01499","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:2887893637","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1808.01499.pdf","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":"pmh:oai:econstor.eu:10419/201614","is_oa":false,"landing_page_url":"http://hdl.handle.net/10419/201614","pdf_url":null,"source":{"id":"https://openalex.org/S4306401696","display_name":"Econstor (Econstor)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"doc-type:workingPaper"},{"id":"pmh:oai:pub.uni-bielefeld.de:2933813","is_oa":true,"landing_page_url":"https://pub.uni-bielefeld.de/record/2933813","pdf_url":null,"source":{"id":"https://openalex.org/S4306401670","display_name":"PUB \u2013 Publications at Bielefeld University (Bielefeld University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I20121455","host_organization_name":"Bielefeld University","host_organization_lineage":["https://openalex.org/I20121455"],"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":"http://purl.org/coar/resource_type/c_8042"},{"id":"pmh:oai:pub.uni-bielefeld.de:2944790","is_oa":false,"landing_page_url":"https://pub.uni-bielefeld.de/record/2944790","pdf_url":null,"source":{"id":"https://openalex.org/S4306401670","display_name":"PUB \u2013 Publications at Bielefeld University (Bielefeld University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I20121455","host_organization_name":"Bielefeld University","host_organization_lineage":["https://openalex.org/I20121455"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"http://purl.org/coar/resource_type/c_6501"},{"id":"pmh:oai:qmro.qmul.ac.uk:123456789/62097","is_oa":false,"landing_page_url":"https://qmro.qmul.ac.uk/xmlui/handle/123456789/62097","pdf_url":null,"source":{"id":"https://openalex.org/S4306400530","display_name":"Queen Mary Research Online (Queen Mary University of London)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I166337079","host_organization_name":"Queen Mary University of London","host_organization_lineage":["https://openalex.org/I166337079"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Article"},{"id":"doi:10.48550/arxiv.1808.01499","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1808.01499","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:1808.01499","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1808.01499","pdf_url":"https://arxiv.org/pdf/1808.01499","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":[{"id":"https://metadata.un.org/sdg/8","score":0.6700000166893005,"display_name":"Decent work and economic growth"}],"awards":[{"id":"https://openalex.org/G2201079836","display_name":null,"funder_award_id":"EP/P017193/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G6052429835","display_name":null,"funder_award_id":"(DFG)","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"}],"funders":[{"id":"https://openalex.org/F4320320879","display_name":"Deutsche Forschungsgemeinschaft","ror":"https://ror.org/018mejw64"},{"id":"https://openalex.org/F4320334627","display_name":"Engineering and Physical Sciences Research Council","ror":"https://ror.org/0439y7842"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2887893637.pdf","grobid_xml":"https://content.openalex.org/works/W2887893637.grobid-xml"},"referenced_works_count":26,"referenced_works":["https://openalex.org/W604762380","https://openalex.org/W1485598997","https://openalex.org/W1558902221","https://openalex.org/W1583915406","https://openalex.org/W1974932729","https://openalex.org/W1983819214","https://openalex.org/W1995503011","https://openalex.org/W2004631194","https://openalex.org/W2007849171","https://openalex.org/W2017906978","https://openalex.org/W2033780464","https://openalex.org/W2058823784","https://openalex.org/W2061825652","https://openalex.org/W2079246218","https://openalex.org/W2115251869","https://openalex.org/W2132565565","https://openalex.org/W2157757184","https://openalex.org/W2217046481","https://openalex.org/W2282780505","https://openalex.org/W2902606947","https://openalex.org/W2962907402","https://openalex.org/W3087312812","https://openalex.org/W3121713678","https://openalex.org/W3124311599","https://openalex.org/W3125159644","https://openalex.org/W3126061707"],"related_works":["https://openalex.org/W3121379310","https://openalex.org/W3125397090","https://openalex.org/W2912111663","https://openalex.org/W2551939582","https://openalex.org/W2164334093","https://openalex.org/W2521526399","https://openalex.org/W1875946268","https://openalex.org/W2132529433","https://openalex.org/W3159436497","https://openalex.org/W2014838013","https://openalex.org/W3015096560","https://openalex.org/W2189116695","https://openalex.org/W2622190498","https://openalex.org/W2898473889","https://openalex.org/W1983819214","https://openalex.org/W3122887322","https://openalex.org/W1566921895","https://openalex.org/W3126068793","https://openalex.org/W3214322321","https://openalex.org/W1977086132"],"abstract_inverted_index":{"We":[0],"solve":[1],"an":[2,65,128],"infinite":[3],"time-horizon":[4],"bounded-variation":[5],"stochastic":[6],"control":[7,27],"problem":[8,20],"with":[9,76,150,153,166,198,227],"regime":[10,151],"switching":[11,152],"between":[12],"$N$":[13,77,154],"states.":[14,78],"This":[15],"is":[16,120],"motivated":[17],"by":[18,49,64,71,87,212],"the":[19,28,38,50,58,84,124,134,137,169,180,218,221,230],"of":[21,57,61,136,162,171,194,220],"a":[22,72,98,107,112,145,160,175,191,195,203,213],"government":[23,54,80],"that":[24,118],"wants":[25],"to":[26,122,229],"country's":[29],"debt-to-GDP":[30,39,125],"(gross":[31],"domestic":[32],"product)":[33],"ratio.":[34],"In":[35],"our":[36,172,188,209],"formulation,":[37],"ratio":[40,126,224],"evolves":[41],"stochastically":[42],"in":[43,127,186,190],"continuous":[44],"time,":[45],"and":[46,93,156,206],"its":[47,91],"drift---given":[48],"interest":[51],"rate":[52,60],"on":[53,83,106,133,217],"debt,":[55],"net":[56,99],"growth":[59],"GDP---is":[62],"affected":[63],"exogenous":[66],"macroeconomic":[67],"risk":[68,138],"process":[69],"modelled":[70],"continuous-time":[73],"Markov":[74,196],"chain":[75,197],"The":[79],"can":[81],"act":[82],"public":[85],"debt":[86,223],"increasing":[88],"or":[89],"decreasing":[90],"level,":[92],"it":[94,119],"aims":[95],"at":[96],"minimizing":[97],"expected":[100],"regime-dependent":[101],"cost":[102],"functional.":[103],"Without":[104],"relying":[105],"guess-and-verify":[108],"approach,":[109],"but":[110],"performing":[111],"direct":[113],"probabilistic":[114],"study,":[115],"we":[116,184,201,207],"show":[117],"optimal":[121,147,222],"keep":[123],"interval,":[129],"whose":[130],"boundaries":[131,141],"depend":[132],"states":[135,155],"process.":[139],"These":[140],"are":[142,157],"given":[143],"through":[144,159],"zero-sum":[146],"stopping":[148],"game":[149],"characterized":[158],"system":[161],"nonlinear":[163],"algebraic":[164],"equations":[165],"constraints.":[167],"To":[168],"best":[170],"knowledge,":[173],"such":[174],"result":[176],"appears":[177],"here":[178],"for":[179],"first":[181],"time.":[182],"Finally,":[183],"put":[185],"practice":[187],"methodology":[189],"case":[192],"study":[193,216],"$N=2$":[199],"states;":[200],"provide":[202],"thorough":[204],"analysis":[205],"complement":[208],"theoretical":[210],"results":[211],"detailed":[214],"numerical":[215],"sensitivity":[219],"management":[225],"policy":[226],"respect":[228],"problem's":[231],"parameters.":[232]},"counts_by_year":[],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2025-10-10T00:00:00"}