{"id":"https://openalex.org/W4415967726","doi":"https://doi.org/10.3390/sym17111892","title":"Incorporating Parameter Uncertainty into Copula Models: A Fuzzy Approach","display_name":"Incorporating Parameter Uncertainty into Copula Models: A Fuzzy Approach","publication_year":2025,"publication_date":"2025-11-06","ids":{"openalex":"https://openalex.org/W4415967726","doi":"https://doi.org/10.3390/sym17111892"},"language":"en","primary_location":{"id":"doi:10.3390/sym17111892","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym17111892","pdf_url":"https://www.mdpi.com/2073-8994/17/11/1892/pdf?version=1762427084","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2073-8994/17/11/1892/pdf?version=1762427084","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5014427304","display_name":"Irina Georgescu","orcid":"https://orcid.org/0000-0002-8536-5636"},"institutions":[{"id":"https://openalex.org/I88491126","display_name":"Bucharest University of Economic Studies","ror":"https://ror.org/04yvncj21","country_code":"RO","type":"education","lineage":["https://openalex.org/I88491126"]}],"countries":["RO"],"is_corresponding":true,"raw_author_name":"Irina Georgescu","raw_affiliation_strings":["Department of Economic Informatics and Cybernetics, Bucharest University of Economic Studies, 0105552 Bucharest, Romania"],"raw_orcid":"https://orcid.org/0000-0002-8536-5636","affiliations":[{"raw_affiliation_string":"Department of Economic Informatics and Cybernetics, Bucharest University of Economic Studies, 0105552 Bucharest, Romania","institution_ids":["https://openalex.org/I88491126"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5020175868","display_name":"Jani Kinnunen","orcid":"https://orcid.org/0000-0002-0154-6617"},"institutions":[{"id":"https://openalex.org/I63548447","display_name":"Lappeenranta-Lahti University of Technology","ror":"https://ror.org/0208vgz68","country_code":"FI","type":"education","lineage":["https://openalex.org/I63548447"]}],"countries":["FI"],"is_corresponding":true,"raw_author_name":"Jani Kinnunen","raw_affiliation_strings":["LUT Business School, LUT University, Yliopistonkatu 31, 53851 Lappeenranta, Finland"],"raw_orcid":"https://orcid.org/0000-0002-0154-6617","affiliations":[{"raw_affiliation_string":"LUT Business School, LUT University, Yliopistonkatu 31, 53851 Lappeenranta, Finland","institution_ids":["https://openalex.org/I63548447"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5014427304","https://openalex.org/A5020175868"],"corresponding_institution_ids":["https://openalex.org/I63548447","https://openalex.org/I88491126"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":1.766,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.87965023,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":95,"max":98},"biblio":{"volume":"17","issue":"11","first_page":"1892","last_page":"1892"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10282","display_name":"Financial Risk and Volatility Modeling","score":0.6492999792098999,"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/T10282","display_name":"Financial Risk and Volatility Modeling","score":0.6492999792098999,"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/T11059","display_name":"Market Dynamics and Volatility","score":0.20730000734329224,"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":0.06909999996423721,"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/cvar","display_name":"CVAR","score":0.8909000158309937},{"id":"https://openalex.org/keywords/copula","display_name":"Copula (linguistics)","score":0.7182999849319458},{"id":"https://openalex.org/keywords/fuzzy-logic","display_name":"Fuzzy logic","score":0.6524999737739563},{"id":"https://openalex.org/keywords/fuzzy-set","display_name":"Fuzzy set","score":0.47049999237060547},{"id":"https://openalex.org/keywords/gaussian","display_name":"Gaussian","score":0.4287000000476837},{"id":"https://openalex.org/keywords/fuzzy-number","display_name":"Fuzzy number","score":0.42329999804496765},{"id":"https://openalex.org/keywords/estimation-theory","display_name":"Estimation theory","score":0.40619999170303345},{"id":"https://openalex.org/keywords/vine-copula","display_name":"Vine copula","score":0.38190001249313354}],"concepts":[{"id":"https://openalex.org/C2779922397","wikidata":"https://www.wikidata.org/wiki/Q5014755","display_name":"CVAR","level":4,"score":0.8909000158309937},{"id":"https://openalex.org/C17618745","wikidata":"https://www.wikidata.org/wiki/Q207509","display_name":"Copula (linguistics)","level":2,"score":0.7182999849319458},{"id":"https://openalex.org/C58166","wikidata":"https://www.wikidata.org/wiki/Q224821","display_name":"Fuzzy logic","level":2,"score":0.6524999737739563},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5212000012397766},{"id":"https://openalex.org/C149782125","wikidata":"https://www.wikidata.org/wiki/Q160039","display_name":"Econometrics","level":1,"score":0.4749000072479248},{"id":"https://openalex.org/C42011625","wikidata":"https://www.wikidata.org/wiki/Q1055058","display_name":"Fuzzy set","level":3,"score":0.47049999237060547},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4489000141620636},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.4287000000476837},{"id":"https://openalex.org/C1883856","wikidata":"https://www.wikidata.org/wiki/Q3407463","display_name":"Fuzzy number","level":4,"score":0.42329999804496765},{"id":"https://openalex.org/C167928553","wikidata":"https://www.wikidata.org/wiki/Q1376021","display_name":"Estimation theory","level":2,"score":0.40619999170303345},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.38429999351501465},{"id":"https://openalex.org/C2779676228","wikidata":"https://www.wikidata.org/wiki/Q25303905","display_name":"Vine copula","level":3,"score":0.38190001249313354},{"id":"https://openalex.org/C63479239","wikidata":"https://www.wikidata.org/wiki/Q7353546","display_name":"Robustness (evolution)","level":3,"score":0.3723999857902527},{"id":"https://openalex.org/C118671147","wikidata":"https://www.wikidata.org/wiki/Q578714","display_name":"Quantile","level":2,"score":0.36809998750686646},{"id":"https://openalex.org/C170260401","wikidata":"https://www.wikidata.org/wiki/Q5251735","display_name":"Defuzzification","level":5,"score":0.34860000014305115},{"id":"https://openalex.org/C41426520","wikidata":"https://www.wikidata.org/wiki/Q1192065","display_name":"Point estimation","level":2,"score":0.3368000090122223},{"id":"https://openalex.org/C2781472820","wikidata":"https://www.wikidata.org/wiki/Q2154759","display_name":"Risk measure","level":3,"score":0.335999995470047},{"id":"https://openalex.org/C5496284","wikidata":"https://www.wikidata.org/wiki/Q5420856","display_name":"Expected shortfall","level":3,"score":0.30649998784065247},{"id":"https://openalex.org/C2776719154","wikidata":"https://www.wikidata.org/wiki/Q1094965","display_name":"Downside risk","level":3,"score":0.25540000200271606},{"id":"https://openalex.org/C148671577","wikidata":"https://www.wikidata.org/wiki/Q5511133","display_name":"Fuzzy set operations","level":4,"score":0.25429999828338623},{"id":"https://openalex.org/C195975749","wikidata":"https://www.wikidata.org/wiki/Q1475705","display_name":"Fuzzy control system","level":3,"score":0.2540000081062317},{"id":"https://openalex.org/C147581598","wikidata":"https://www.wikidata.org/wiki/Q729429","display_name":"Extreme value theory","level":2,"score":0.2513999938964844},{"id":"https://openalex.org/C106306483","wikidata":"https://www.wikidata.org/wiki/Q183984","display_name":"Futures contract","level":2,"score":0.2500999867916107}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.3390/sym17111892","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym17111892","pdf_url":"https://www.mdpi.com/2073-8994/17/11/1892/pdf?version=1762427084","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.3390/sym17111892","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym17111892","pdf_url":"https://www.mdpi.com/2073-8994/17/11/1892/pdf?version=1762427084","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4415967726.pdf","grobid_xml":"https://content.openalex.org/works/W4415967726.grobid-xml"},"referenced_works_count":24,"referenced_works":["https://openalex.org/W74954028","https://openalex.org/W2019291268","https://openalex.org/W2054957279","https://openalex.org/W2127958806","https://openalex.org/W3013703284","https://openalex.org/W3017080297","https://openalex.org/W3022286337","https://openalex.org/W3036077225","https://openalex.org/W3158113069","https://openalex.org/W3184634011","https://openalex.org/W3210004592","https://openalex.org/W4206032536","https://openalex.org/W4211007335","https://openalex.org/W4214597110","https://openalex.org/W4239304079","https://openalex.org/W4248681815","https://openalex.org/W4292158025","https://openalex.org/W4315490266","https://openalex.org/W4360869630","https://openalex.org/W4381165546","https://openalex.org/W4385980208","https://openalex.org/W4392886703","https://openalex.org/W4404738350","https://openalex.org/W4414020319"],"related_works":[],"abstract_inverted_index":{"This":[0,45,151],"paper":[1],"proposes":[2],"a":[3,54],"fuzzy":[4,28,55,98,129,132,143,157,160],"copula-based":[5],"optimization":[6,56,158],"framework":[7,100],"for":[8,166],"modeling":[9,162],"dependence":[10,43,113,137,161],"structures":[11],"and":[12,30,38,70,83,85,91,119,131,139,159,169],"financial":[13,174],"risk":[14,120,149],"under":[15],"parameter":[16],"uncertainty.":[17],"The":[18,63,93],"parameters":[19,52],"of":[20,41,50,156],"selected":[21],"copula":[22,51,99],"families":[23],"are":[24],"represented":[25],"as":[26,163],"trapezoidal":[27],"numbers,":[29],"their":[31],"\u03b1-cut":[32],"intervals":[33],"capture":[34,135],"both":[35],"the":[36,48,97,154],"support":[37],"core":[39],"ranges":[40],"plausible":[42],"values.":[44],"fuzzification":[46],"transforms":[47],"estimation":[49,107],"into":[53],"problem,":[57],"enhancing":[58],"robustness":[59],"against":[60],"sampling":[61],"variability.":[62],"methodology":[64],"is":[65],"empirically":[66],"applied":[67],"to":[68],"gold":[69],"oil":[71],"futures":[72],"(1":[73],"January":[74,76],"2015\u20131":[75],"2025),":[77],"comparing":[78],"symmetric":[79],"copulas,":[80,87],"i.e.,":[81,88],"Gaussian":[82],"Frank":[84],"asymmetric":[86],"Clayton,":[89],"Gumbel":[90],"Student-t.":[92],"results":[94],"prove":[95],"that":[96,128],"provides":[101],"richer":[102],"insights":[103],"than":[104],"classical":[105],"point":[106],"by":[108],"explicitly":[109],"expressing":[110],"uncertainty":[111,168],"in":[112,173],"measures":[114],"(Kendall\u2019s":[115],"\u03c4,":[116],"Spearman\u2019s":[117],"\u03c1)":[118],"indicators":[121],"(Value-at-Risk,":[122],"Conditional":[123],"Value-at-Risk).":[124],"Rolling-window":[125],"analyses":[126],"reveal":[127],"VaR":[130],"CVaR":[133,144],"effectively":[134],"temporal":[136],"shifts":[138],"tail":[140],"severity,":[141],"with":[142],"consistently":[145],"producing":[146],"more":[147],"conservative":[148],"estimates.":[150],"study":[152],"highlights":[153],"potential":[155],"powerful":[164],"tools":[165],"quantifying":[167],"managing":[170],"extreme":[171],"co-movements":[172],"markets.":[175]},"counts_by_year":[{"year":2026,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-11-06T00:00:00"}