{"id":"https://openalex.org/W4280642840","doi":"https://doi.org/10.3390/sym14051041","title":"A Structural Credit Risk Model Driven by the L\u00e9vy Process under Knightian Uncertainty","display_name":"A Structural Credit Risk Model Driven by the L\u00e9vy Process under Knightian Uncertainty","publication_year":2022,"publication_date":"2022-05-19","ids":{"openalex":"https://openalex.org/W4280642840","doi":"https://doi.org/10.3390/sym14051041"},"language":"en","primary_location":{"id":"doi:10.3390/sym14051041","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym14051041","pdf_url":"https://www.mdpi.com/2073-8994/14/5/1041/pdf?version=1652956469","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","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2073-8994/14/5/1041/pdf?version=1652956469","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5101800745","display_name":"Hong Huang","orcid":"https://orcid.org/0000-0002-7746-0393"},"institutions":[{"id":"https://openalex.org/I34949971","display_name":"University of Jinan","ror":"https://ror.org/02mjz6f26","country_code":"CN","type":"education","lineage":["https://openalex.org/I34949971"]},{"id":"https://openalex.org/I4210150411","display_name":"Shandong Youth University of Political Science","ror":"https://ror.org/04bwp4t29","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210150411"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Hong Huang","raw_affiliation_strings":["Key Laboratory of Intelligent Information Processing Technology and Security, Universities of Shandong, Jinan 250103, China","School of Information Engineering, Shandong Youth University of Political Science, Jinan 250103, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Key Laboratory of Intelligent Information Processing Technology and Security, Universities of Shandong, Jinan 250103, China","institution_ids":["https://openalex.org/I34949971"]},{"raw_affiliation_string":"School of Information Engineering, Shandong Youth University of Political Science, Jinan 250103, China","institution_ids":["https://openalex.org/I4210150411"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5021207605","display_name":"Yufu Ning","orcid":"https://orcid.org/0000-0002-7230-4017"},"institutions":[{"id":"https://openalex.org/I34949971","display_name":"University of Jinan","ror":"https://ror.org/02mjz6f26","country_code":"CN","type":"education","lineage":["https://openalex.org/I34949971"]},{"id":"https://openalex.org/I4210150411","display_name":"Shandong Youth University of Political Science","ror":"https://ror.org/04bwp4t29","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210150411"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Yufu Ning","raw_affiliation_strings":["Key Laboratory of Intelligent Information Processing Technology and Security, Universities of Shandong, Jinan 250103, China","School of Information Engineering, Shandong Youth University of Political Science, Jinan 250103, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Key Laboratory of Intelligent Information Processing Technology and Security, Universities of Shandong, Jinan 250103, China","institution_ids":["https://openalex.org/I34949971"]},{"raw_affiliation_string":"School of Information Engineering, Shandong Youth University of Political Science, Jinan 250103, China","institution_ids":["https://openalex.org/I4210150411"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5057396938","display_name":"Xiu\u2010Mei Chen","orcid":"https://orcid.org/0000-0001-9635-5292"},"institutions":[{"id":"https://openalex.org/I34949971","display_name":"University of Jinan","ror":"https://ror.org/02mjz6f26","country_code":"CN","type":"education","lineage":["https://openalex.org/I34949971"]},{"id":"https://openalex.org/I4210150411","display_name":"Shandong Youth University of Political Science","ror":"https://ror.org/04bwp4t29","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210150411"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xiumei Chen","raw_affiliation_strings":["Key Laboratory of Intelligent Information Processing Technology and Security, Universities of Shandong, Jinan 250103, China","School of Information Engineering, Shandong Youth University of Political Science, Jinan 250103, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Key Laboratory of Intelligent Information Processing Technology and Security, Universities of Shandong, Jinan 250103, China","institution_ids":["https://openalex.org/I34949971"]},{"raw_affiliation_string":"School of Information Engineering, Shandong Youth University of Political Science, Jinan 250103, China","institution_ids":["https://openalex.org/I4210150411"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5021207605"],"corresponding_institution_ids":["https://openalex.org/I34949971","https://openalex.org/I4210150411"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":0.6354,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.69290022,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":96,"max":97},"biblio":{"volume":"14","issue":"5","first_page":"1041","last_page":"1041"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11496","display_name":"Credit Risk and Financial Regulations","score":0.9987999796867371,"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/T11496","display_name":"Credit Risk and Financial Regulations","score":0.9987999796867371,"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/T10067","display_name":"Stochastic processes and financial applications","score":0.9980000257492065,"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/T10282","display_name":"Financial Risk and Volatility Modeling","score":0.9947999715805054,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/knightian-uncertainty","display_name":"Knightian uncertainty","score":0.8187216520309448},{"id":"https://openalex.org/keywords/econometrics","display_name":"Econometrics","score":0.5488831996917725},{"id":"https://openalex.org/keywords/economics","display_name":"Economics","score":0.4883579909801483},{"id":"https://openalex.org/keywords/jump","display_name":"Jump","score":0.48571687936782837},{"id":"https://openalex.org/keywords/credit-risk","display_name":"Credit risk","score":0.4731146991252899},{"id":"https://openalex.org/keywords/risk-neutral-measure","display_name":"Risk-neutral measure","score":0.4292924404144287},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.396878719329834},{"id":"https://openalex.org/keywords/actuarial-science","display_name":"Actuarial science","score":0.34257906675338745},{"id":"https://openalex.org/keywords/mathematical-economics","display_name":"Mathematical economics","score":0.3359858989715576},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.23862051963806152},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.12774717807769775}],"concepts":[{"id":"https://openalex.org/C2779652836","wikidata":"https://www.wikidata.org/wiki/Q1548830","display_name":"Knightian uncertainty","level":3,"score":0.8187216520309448},{"id":"https://openalex.org/C149782125","wikidata":"https://www.wikidata.org/wiki/Q160039","display_name":"Econometrics","level":1,"score":0.5488831996917725},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.4883579909801483},{"id":"https://openalex.org/C2780695682","wikidata":"https://www.wikidata.org/wiki/Q4005959","display_name":"Jump","level":2,"score":0.48571687936782837},{"id":"https://openalex.org/C178350159","wikidata":"https://www.wikidata.org/wiki/Q162714","display_name":"Credit risk","level":2,"score":0.4731146991252899},{"id":"https://openalex.org/C85106312","wikidata":"https://www.wikidata.org/wiki/Q1058362","display_name":"Risk-neutral measure","level":2,"score":0.4292924404144287},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.396878719329834},{"id":"https://openalex.org/C162118730","wikidata":"https://www.wikidata.org/wiki/Q1128453","display_name":"Actuarial science","level":1,"score":0.34257906675338745},{"id":"https://openalex.org/C144237770","wikidata":"https://www.wikidata.org/wiki/Q747534","display_name":"Mathematical economics","level":1,"score":0.3359858989715576},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.23862051963806152},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.12774717807769775},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C2780522230","wikidata":"https://www.wikidata.org/wiki/Q1140419","display_name":"Ambiguity","level":2,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/sym14051041","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym14051041","pdf_url":"https://www.mdpi.com/2073-8994/14/5/1041/pdf?version=1652956469","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"},{"id":"pmh:oai:doaj.org/article:d476487e5b684db08fa562649a6c159f","is_oa":true,"landing_page_url":"https://doaj.org/article/d476487e5b684db08fa562649a6c159f","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,"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":"Symmetry, Vol 14, Iss 5, p 1041 (2022)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2073-8994/14/5/1041/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/sym14051041","pdf_url":null,"source":{"id":"https://openalex.org/S4306400947","display_name":"MDPI (MDPI AG)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210097602","host_organization_name":"Multidisciplinary Digital Publishing Institute (Switzerland)","host_organization_lineage":["https://openalex.org/I4210097602"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Symmetry","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/sym14051041","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym14051041","pdf_url":"https://www.mdpi.com/2073-8994/14/5/1041/pdf?version=1652956469","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":[{"display_name":"Peace, Justice and strong institutions","score":0.5,"id":"https://metadata.un.org/sdg/16"}],"awards":[{"id":"https://openalex.org/G1035825296","display_name":null,"funder_award_id":"ZR2019BG015","funder_id":"https://openalex.org/F4320324174","funder_display_name":"Natural Science Foundation of Shandong Province"}],"funders":[{"id":"https://openalex.org/F4320324174","display_name":"Natural Science Foundation of Shandong Province","ror":null}],"has_content":{"pdf":true,"grobid_xml":false},"content_urls":{"pdf":"https://content.openalex.org/works/W4280642840.pdf"},"referenced_works_count":13,"referenced_works":["https://openalex.org/W2018881312","https://openalex.org/W2027047704","https://openalex.org/W2056998793","https://openalex.org/W2077791698","https://openalex.org/W2092200574","https://openalex.org/W2105973145","https://openalex.org/W2138765659","https://openalex.org/W2163991121","https://openalex.org/W2352028954","https://openalex.org/W2379378992","https://openalex.org/W2391379114","https://openalex.org/W3007171935","https://openalex.org/W6675975338"],"related_works":["https://openalex.org/W2923494830","https://openalex.org/W1577857700","https://openalex.org/W3124056384","https://openalex.org/W2042055575","https://openalex.org/W2093110095","https://openalex.org/W2012206417","https://openalex.org/W4280642840","https://openalex.org/W3121878783","https://openalex.org/W1540777668","https://openalex.org/W2973906818"],"abstract_inverted_index":{"The":[0,156],"classic":[1],"credit":[2,73],"risk":[3,74],"structured":[4],"model":[5,75],"assumes":[6],"that":[7,59,159],"risky":[8,18],"asset":[9,19],"values":[10,20,104,148,170],"obey":[11],"geometric":[12],"Brownian":[13],"motion.":[14],"In":[15,108,183],"reality,":[16],"however,":[17],"are":[21,51],"often":[22],"not":[23],"a":[24,64,71,130,174],"continuous":[25],"and":[26,35,43,92,102,146,168,211],"symmetrical":[27],"process,":[28],"but":[29,177],"rather":[30],"they":[31],"appear":[32],"to":[33,128],"jump":[34,124],"have":[36],"asymmetric":[37],"characteristics,":[38],"such":[39],"as":[40],"higher":[41],"peaks":[42],"fat":[44],"tails.":[45],"On":[46],"the":[47,77,84,113,117,123,134,141,160,165,185,190,199,206],"other":[48],"hand,":[49],"there":[50],"real":[52],"Knight":[53,81],"uncertainty":[54,139],"risks":[55],"in":[56,76,192],"financial":[57],"markets":[58],"cannot":[60],"be":[61],"measured":[62],"by":[63],"single":[65],"probability":[66,145,162],"measure.":[67],"This":[68,195],"work":[69],"examined":[70],"structural":[72],"L\u00e9vy":[78],"market":[79,203],"under":[80,180],"uncertainty.":[82,182,194],"Using":[83],"L\u00e9vy\u2013Laplace":[85],"exponent,":[86],"we":[87,110],"established":[88],"dynamic":[89],"pricing":[90,142],"models":[91],"obtained":[93],"intervals":[94],"of":[95,105,137,143,149,163,201,209],"prices":[96],"for":[97,116,215],"default":[98,144,161],"probability,":[99],"stock":[100,147,166],"values,":[101,167],"bond":[103,169],"enterprise,":[106,164],"respectively.":[107],"particular,":[109],"also":[111],"proved":[112],"explicit":[114],"solutions":[115],"three":[118],"value":[119,208],"processes":[120],"above":[121],"when":[122],"process":[125],"is":[126],"assumed":[127],"follow":[129],"log-normal":[131],"distribution.":[132],"Finally,":[133],"important":[135],"impacts":[136],"Knightian":[138,181,193],"on":[140,205],"enterprise":[150],"were":[151,171],"studied":[152],"through":[153],"numerical":[154],"analysis.":[155],"results":[157],"showed":[158],"no":[172],"longer":[173],"certain":[175],"value,":[176],"an":[178],"interval":[179,186],"addition,":[184],"changed":[187],"continuously":[188],"with":[189],"increase":[191],"result":[196],"better":[197],"reflected":[198],"impact":[200],"different":[202],"sentiments":[204],"equilibrium":[207],"assets,":[210],"expanded":[212],"decision-making":[213],"flexibility":[214],"investors.":[216]},"counts_by_year":[{"year":2025,"cited_by_count":3}],"updated_date":"2026-05-22T06:13:13.366637","created_date":"2025-10-10T00:00:00"}
