{"id":"https://openalex.org/W2954752743","doi":"https://doi.org/10.3390/e21070634","title":"Divergence-Based Risk Measures: A Discussion on Sensitivities and Extensions","display_name":"Divergence-Based Risk Measures: A Discussion on Sensitivities and Extensions","publication_year":2019,"publication_date":"2019-06-27","ids":{"openalex":"https://openalex.org/W2954752743","doi":"https://doi.org/10.3390/e21070634","mag":"2954752743","pmid":"https://pubmed.ncbi.nlm.nih.gov/33267348"},"language":"en","primary_location":{"id":"doi:10.3390/e21070634","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e21070634","pdf_url":"https://www.mdpi.com/1099-4300/21/7/634/pdf?version=1561629070","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"is_oa":true,"is_in_doaj":true,"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":"Entropy","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj","pubmed"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/1099-4300/21/7/634/pdf?version=1561629070","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5008621958","display_name":"Meng Xu","orcid":"https://orcid.org/0000-0002-0544-3842"},"institutions":[{"id":"https://openalex.org/I24185976","display_name":"Sichuan University","ror":"https://ror.org/011ashp19","country_code":"CN","type":"education","lineage":["https://openalex.org/I24185976"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Meng Xu","raw_affiliation_strings":["School of Economics, Sichuan University, Chengdu 610065, China"],"raw_orcid":"https://orcid.org/0000-0002-0544-3842","affiliations":[{"raw_affiliation_string":"School of Economics, Sichuan University, Chengdu 610065, China","institution_ids":["https://openalex.org/I24185976"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5055610180","display_name":"J. M. Angulo","orcid":"https://orcid.org/0000-0002-6863-7847"},"institutions":[{"id":"https://openalex.org/I173304897","display_name":"Universidad de Granada","ror":"https://ror.org/04njjy449","country_code":"ES","type":"education","lineage":["https://openalex.org/I173304897"]}],"countries":["ES"],"is_corresponding":true,"raw_author_name":"Jos\u00e9 M. Angulo","raw_affiliation_strings":["Department of Statistics and Operations Research, University of Granada, 18071 Granada, Spain"],"raw_orcid":"https://orcid.org/0000-0002-6863-7847","affiliations":[{"raw_affiliation_string":"Department of Statistics and Operations Research, University of Granada, 18071 Granada, Spain","institution_ids":["https://openalex.org/I173304897"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5055610180"],"corresponding_institution_ids":["https://openalex.org/I173304897"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":0.6173,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.72866023,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":96},"biblio":{"volume":"21","issue":"7","first_page":"634","last_page":"634"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11413","display_name":"Risk and Portfolio Optimization","score":0.9984999895095825,"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"}},"topics":[{"id":"https://openalex.org/T11413","display_name":"Risk and Portfolio Optimization","score":0.9984999895095825,"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"}},{"id":"https://openalex.org/T10050","display_name":"Multi-Criteria Decision Making","score":0.9925000071525574,"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"}},{"id":"https://openalex.org/T12135","display_name":"Fuzzy Systems and Optimization","score":0.9739000201225281,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/divergence","display_name":"Divergence (linguistics)","score":0.7732640504837036},{"id":"https://openalex.org/keywords/measure","display_name":"Measure (data warehouse)","score":0.6687317490577698},{"id":"https://openalex.org/keywords/risk-measure","display_name":"Risk measure","score":0.6677367687225342},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6193408966064453},{"id":"https://openalex.org/keywords/coherent-risk-measure","display_name":"Coherent risk measure","score":0.5947616100311279},{"id":"https://openalex.org/keywords/dynamic-risk-measure","display_name":"Dynamic risk measure","score":0.5590580105781555},{"id":"https://openalex.org/keywords/kullback\u2013leibler-divergence","display_name":"Kullback\u2013Leibler divergence","score":0.5118700861930847},{"id":"https://openalex.org/keywords/sensitivity","display_name":"Sensitivity (control systems)","score":0.49664026498794556},{"id":"https://openalex.org/keywords/probability-measure","display_name":"Probability measure","score":0.485313355922699},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4434794485569},{"id":"https://openalex.org/keywords/econometrics","display_name":"Econometrics","score":0.33485788106918335},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.33477482199668884},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2942361533641815},{"id":"https://openalex.org/keywords/data-mining","display_name":"Data mining","score":0.0973401665687561},{"id":"https://openalex.org/keywords/economics","display_name":"Economics","score":0.09117990732192993},{"id":"https://openalex.org/keywords/finance","display_name":"Finance","score":0.07646158337593079}],"concepts":[{"id":"https://openalex.org/C207390915","wikidata":"https://www.wikidata.org/wiki/Q1230525","display_name":"Divergence (linguistics)","level":2,"score":0.7732640504837036},{"id":"https://openalex.org/C2780009758","wikidata":"https://www.wikidata.org/wiki/Q6804172","display_name":"Measure (data warehouse)","level":2,"score":0.6687317490577698},{"id":"https://openalex.org/C2781472820","wikidata":"https://www.wikidata.org/wiki/Q2154759","display_name":"Risk measure","level":3,"score":0.6677367687225342},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6193408966064453},{"id":"https://openalex.org/C148845407","wikidata":"https://www.wikidata.org/wiki/Q5141358","display_name":"Coherent risk measure","level":4,"score":0.5947616100311279},{"id":"https://openalex.org/C167548438","wikidata":"https://www.wikidata.org/wiki/Q5319012","display_name":"Dynamic risk measure","level":4,"score":0.5590580105781555},{"id":"https://openalex.org/C171752962","wikidata":"https://www.wikidata.org/wiki/Q255166","display_name":"Kullback\u2013Leibler divergence","level":2,"score":0.5118700861930847},{"id":"https://openalex.org/C21200559","wikidata":"https://www.wikidata.org/wiki/Q7451068","display_name":"Sensitivity (control systems)","level":2,"score":0.49664026498794556},{"id":"https://openalex.org/C21031990","wikidata":"https://www.wikidata.org/wiki/Q355020","display_name":"Probability measure","level":2,"score":0.485313355922699},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4434794485569},{"id":"https://openalex.org/C149782125","wikidata":"https://www.wikidata.org/wiki/Q160039","display_name":"Econometrics","level":1,"score":0.33485788106918335},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.33477482199668884},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2942361533641815},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.0973401665687561},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.09117990732192993},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.07646158337593079},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0},{"id":"https://openalex.org/C2780821815","wikidata":"https://www.wikidata.org/wiki/Q5340806","display_name":"Portfolio","level":2,"score":0.0},{"id":"https://openalex.org/C24326235","wikidata":"https://www.wikidata.org/wiki/Q126095","display_name":"Electronic engineering","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0}],"mesh":[],"locations_count":6,"locations":[{"id":"doi:10.3390/e21070634","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e21070634","pdf_url":"https://www.mdpi.com/1099-4300/21/7/634/pdf?version=1561629070","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"is_oa":true,"is_in_doaj":true,"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":"Entropy","raw_type":"journal-article"},{"id":"pmid:33267348","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/33267348","pdf_url":null,"source":{"id":"https://openalex.org/S4306525036","display_name":"PubMed","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy (Basel, Switzerland)","raw_type":null},{"id":"pmh:oai:digibug.ugr.es:10481/61585","is_oa":true,"landing_page_url":"http://hdl.handle.net/10481/61585","pdf_url":null,"source":{"id":"https://openalex.org/S4306400567","display_name":"Institutional Repository of the University of Granada (University of Granada)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I173304897","host_organization_name":"Universidad de Granada","host_organization_lineage":["https://openalex.org/I173304897"],"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":"","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:doaj.org/article:20d75828d9b64de881ca1cfaa549fd7b","is_oa":true,"landing_page_url":"https://doaj.org/article/20d75828d9b64de881ca1cfaa549fd7b","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":"Entropy, Vol 21, Iss 7, p 634 (2019)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/1099-4300/21/7/634/","is_oa":true,"landing_page_url":"http://dx.doi.org/10.3390/e21070634","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":"Entropy","raw_type":"Text"},{"id":"pmh:oai:pubmedcentral.nih.gov:7515127","is_oa":true,"landing_page_url":"https://www.ncbi.nlm.nih.gov/pmc/articles/7515127","pdf_url":null,"source":{"id":"https://openalex.org/S2764455111","display_name":"PubMed Central","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"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":"Entropy (Basel)","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/e21070634","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e21070634","pdf_url":"https://www.mdpi.com/1099-4300/21/7/634/pdf?version=1561629070","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"is_oa":true,"is_in_doaj":true,"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":"Entropy","raw_type":"journal-article"},"sustainable_development_goals":[{"score":0.4300000071525574,"display_name":"Decent work and economic growth","id":"https://metadata.un.org/sdg/8"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":48,"referenced_works":["https://openalex.org/W53372922","https://openalex.org/W186520755","https://openalex.org/W925742927","https://openalex.org/W1591570634","https://openalex.org/W1599457284","https://openalex.org/W1727796469","https://openalex.org/W1969897341","https://openalex.org/W1975736346","https://openalex.org/W1975884238","https://openalex.org/W1976406849","https://openalex.org/W1979079176","https://openalex.org/W2004590489","https://openalex.org/W2006218802","https://openalex.org/W2019291268","https://openalex.org/W2021814962","https://openalex.org/W2023958886","https://openalex.org/W2027047704","https://openalex.org/W2031355801","https://openalex.org/W2035516921","https://openalex.org/W2039809383","https://openalex.org/W2054321814","https://openalex.org/W2054456608","https://openalex.org/W2072636537","https://openalex.org/W2075704670","https://openalex.org/W2094060802","https://openalex.org/W2100298399","https://openalex.org/W2129711311","https://openalex.org/W2149497424","https://openalex.org/W2154738336","https://openalex.org/W2165256733","https://openalex.org/W2489822048","https://openalex.org/W2502318419","https://openalex.org/W2616064665","https://openalex.org/W2620090292","https://openalex.org/W2730343460","https://openalex.org/W2775768346","https://openalex.org/W2784539053","https://openalex.org/W2809598557","https://openalex.org/W2950878834","https://openalex.org/W2951905208","https://openalex.org/W2964128834","https://openalex.org/W3122925651","https://openalex.org/W3124098225","https://openalex.org/W3124445206","https://openalex.org/W3127518054","https://openalex.org/W4241080586","https://openalex.org/W4248704747","https://openalex.org/W6748656168"],"related_works":["https://openalex.org/W3125265748","https://openalex.org/W1913405677","https://openalex.org/W2741147126","https://openalex.org/W2998948027","https://openalex.org/W2153969568","https://openalex.org/W2260049256","https://openalex.org/W3125883630","https://openalex.org/W2348792743","https://openalex.org/W4220781592","https://openalex.org/W4379107517"],"abstract_inverted_index":{"This":[0,101],"paper":[1],"introduces":[2],"a":[3,62,105],"new":[4,102],"family":[5,103],"of":[6,29,54,66,108],"the":[7,22,26,30,43,47,55,84],"convex":[8],"divergence-based":[9],"risk":[10,33,73,86,97,110],"measure":[11,34,74,87,98],"by":[12,83],"specifying":[13],"(":[14,67],"h":[15,68],",":[16,69],"\u03d5":[17,70],")":[18,71],"-divergence,":[19],"corresponding":[20],"with":[21,35,75],"dual":[23],"representation.":[24],"First,":[25],"sensitivity":[27,64],"characteristics":[28],"modified":[31],"divergence":[32,109,115],"respect":[36,76],"to":[37,77,114],"profit":[38],"and":[39,42,58,81,95,112],"loss":[40],"(P&L)":[41],"reference":[44],"probability":[45],"in":[46,52],"penalty":[48],"term":[49],"are":[50,99],"discussed,":[51],"view":[53],"certainty":[56],"equivalent":[57],"robust":[59],"statistics.":[60],"Secondly,":[61],"similar":[63],"property":[65],"-divergence":[72],"P&L":[78],"is":[79,88],"shown,":[80],"boundedness":[82],"analytic":[85],"proved.":[89],"Numerical":[90],"studies":[91],"designed":[92],"for":[93],"R\u00e9nyi-":[94],"Tsallis-divergence":[96],"provided.":[100],"integrates":[104],"wide":[106],"spectrum":[107],"measures":[111],"relates":[113],"preferences.":[116]},"counts_by_year":[{"year":2022,"cited_by_count":2},{"year":2019,"cited_by_count":1}],"updated_date":"2026-05-20T08:49:12.498775","created_date":"2025-10-10T00:00:00"}