{"id":"https://openalex.org/W2946148876","doi":"https://doi.org/10.3390/e21050491","title":"Performance of Different Risk Indicators in a Multi-Period Polynomial Portfolio Selection Problem Based on the Credibility Measure","display_name":"Performance of Different Risk Indicators in a Multi-Period Polynomial Portfolio Selection Problem Based on the Credibility Measure","publication_year":2019,"publication_date":"2019-05-13","ids":{"openalex":"https://openalex.org/W2946148876","doi":"https://doi.org/10.3390/e21050491","mag":"2946148876","pmid":"https://pubmed.ncbi.nlm.nih.gov/33267205"},"language":"en","primary_location":{"id":"doi:10.3390/e21050491","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e21050491","pdf_url":"https://www.mdpi.com/1099-4300/21/5/491/pdf?version=1558399768","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/1099-4300/21/5/491/pdf?version=1558399768","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5002127031","display_name":"Jian Zhou","orcid":"https://orcid.org/0000-0001-7835-8879"},"institutions":[{"id":"https://openalex.org/I113940042","display_name":"Shanghai University","ror":"https://ror.org/006teas31","country_code":"CN","type":"education","lineage":["https://openalex.org/I113940042"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jian Zhou","raw_affiliation_strings":["School of Management, Shanghai University, Shanghai 200444, China"],"raw_orcid":"https://orcid.org/0000-0001-7835-8879","affiliations":[{"raw_affiliation_string":"School of Management, Shanghai University, Shanghai 200444, China","institution_ids":["https://openalex.org/I113940042"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101700977","display_name":"Jie Shen","orcid":"https://orcid.org/0000-0002-8959-6626"},"institutions":[{"id":"https://openalex.org/I113940042","display_name":"Shanghai University","ror":"https://ror.org/006teas31","country_code":"CN","type":"education","lineage":["https://openalex.org/I113940042"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jie Shen","raw_affiliation_strings":["School of Management, Shanghai University, Shanghai 200444, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Management, Shanghai University, Shanghai 200444, China","institution_ids":["https://openalex.org/I113940042"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100625274","display_name":"Ziheng Zhao","orcid":"https://orcid.org/0000-0003-3496-3158"},"institutions":[{"id":"https://openalex.org/I181679659","display_name":"Shanghai University of Finance and Economics","ror":"https://ror.org/00wtvfq62","country_code":"CN","type":"education","lineage":["https://openalex.org/I181679659"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Ziheng Zhao","raw_affiliation_strings":["School of Economics, Shanghai University of Finance and Economics, Shanghai 200433, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Economics, Shanghai University of Finance and Economics, Shanghai 200433, China","institution_ids":["https://openalex.org/I181679659"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101506310","display_name":"Yujie Gu","orcid":"https://orcid.org/0000-0002-2670-1919"},"institutions":[{"id":"https://openalex.org/I113940042","display_name":"Shanghai University","ror":"https://ror.org/006teas31","country_code":"CN","type":"education","lineage":["https://openalex.org/I113940042"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yujie Gu","raw_affiliation_strings":["School of Management, Shanghai University, Shanghai 200444, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Management, Shanghai University, Shanghai 200444, China","institution_ids":["https://openalex.org/I113940042"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5074340844","display_name":"Mingxuan Zhao","orcid":"https://orcid.org/0000-0002-5717-9019"},"institutions":[{"id":"https://openalex.org/I116953780","display_name":"Tongji University","ror":"https://ror.org/03rc6as71","country_code":"CN","type":"education","lineage":["https://openalex.org/I116953780"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Mingxuan Zhao","raw_affiliation_strings":["School of Economics and Management, Tongji University, Shanghai 200082, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Economics and Management, Tongji University, Shanghai 200082, China","institution_ids":["https://openalex.org/I116953780"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5074340844"],"corresponding_institution_ids":["https://openalex.org/I116953780"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":0.8429,"has_fulltext":true,"cited_by_count":10,"citation_normalized_percentile":{"value":0.73371473,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":"21","issue":"5","first_page":"491","last_page":"491"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12709","display_name":"Optimization and Mathematical Programming","score":0.9994000196456909,"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"}},"topics":[{"id":"https://openalex.org/T12709","display_name":"Optimization and Mathematical Programming","score":0.9994000196456909,"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"}},{"id":"https://openalex.org/T12135","display_name":"Fuzzy Systems and Optimization","score":0.9980000257492065,"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"}},{"id":"https://openalex.org/T11413","display_name":"Risk and Portfolio Optimization","score":0.9969000220298767,"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/credibility","display_name":"Credibility","score":0.7236902713775635},{"id":"https://openalex.org/keywords/portfolio","display_name":"Portfolio","score":0.7041517496109009},{"id":"https://openalex.org/keywords/risk-measure","display_name":"Risk measure","score":0.6803213357925415},{"id":"https://openalex.org/keywords/selection","display_name":"Selection (genetic algorithm)","score":0.5568163990974426},{"id":"https://openalex.org/keywords/portfolio-optimization","display_name":"Portfolio optimization","score":0.5488989949226379},{"id":"https://openalex.org/keywords/credibility-theory","display_name":"Credibility theory","score":0.5027797222137451},{"id":"https://openalex.org/keywords/entropy","display_name":"Entropy (arrow of time)","score":0.4990119934082031},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.48449990153312683},{"id":"https://openalex.org/keywords/measure","display_name":"Measure (data warehouse)","score":0.4843848645687103},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.4737354516983032},{"id":"https://openalex.org/keywords/spectral-risk-measure","display_name":"Spectral risk measure","score":0.43830686807632446},{"id":"https://openalex.org/keywords/principle-of-maximum-entropy","display_name":"Principle of maximum entropy","score":0.41494446992874146},{"id":"https://openalex.org/keywords/econometrics","display_name":"Econometrics","score":0.40490907430648804},{"id":"https://openalex.org/keywords/actuarial-science","display_name":"Actuarial science","score":0.3758494257926941},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3043469190597534},{"id":"https://openalex.org/keywords/economics","display_name":"Economics","score":0.19730892777442932},{"id":"https://openalex.org/keywords/finance","display_name":"Finance","score":0.18346884846687317},{"id":"https://openalex.org/keywords/data-mining","display_name":"Data mining","score":0.1404179334640503},{"id":"https://openalex.org/keywords/machine-learning","display_name":"Machine learning","score":0.10049861669540405},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.09547629952430725}],"concepts":[{"id":"https://openalex.org/C2780224610","wikidata":"https://www.wikidata.org/wiki/Q1530061","display_name":"Credibility","level":2,"score":0.7236902713775635},{"id":"https://openalex.org/C2780821815","wikidata":"https://www.wikidata.org/wiki/Q5340806","display_name":"Portfolio","level":2,"score":0.7041517496109009},{"id":"https://openalex.org/C2781472820","wikidata":"https://www.wikidata.org/wiki/Q2154759","display_name":"Risk measure","level":3,"score":0.6803213357925415},{"id":"https://openalex.org/C81917197","wikidata":"https://www.wikidata.org/wiki/Q628760","display_name":"Selection (genetic algorithm)","level":2,"score":0.5568163990974426},{"id":"https://openalex.org/C202655437","wikidata":"https://www.wikidata.org/wiki/Q7231728","display_name":"Portfolio optimization","level":3,"score":0.5488989949226379},{"id":"https://openalex.org/C44211194","wikidata":"https://www.wikidata.org/wiki/Q3526803","display_name":"Credibility theory","level":3,"score":0.5027797222137451},{"id":"https://openalex.org/C106301342","wikidata":"https://www.wikidata.org/wiki/Q4117933","display_name":"Entropy (arrow of time)","level":2,"score":0.4990119934082031},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.48449990153312683},{"id":"https://openalex.org/C2780009758","wikidata":"https://www.wikidata.org/wiki/Q6804172","display_name":"Measure (data warehouse)","level":2,"score":0.4843848645687103},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4737354516983032},{"id":"https://openalex.org/C69257216","wikidata":"https://www.wikidata.org/wiki/Q7575204","display_name":"Spectral risk measure","level":4,"score":0.43830686807632446},{"id":"https://openalex.org/C9679016","wikidata":"https://www.wikidata.org/wiki/Q1417473","display_name":"Principle of maximum entropy","level":2,"score":0.41494446992874146},{"id":"https://openalex.org/C149782125","wikidata":"https://www.wikidata.org/wiki/Q160039","display_name":"Econometrics","level":1,"score":0.40490907430648804},{"id":"https://openalex.org/C162118730","wikidata":"https://www.wikidata.org/wiki/Q1128453","display_name":"Actuarial science","level":1,"score":0.3758494257926941},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3043469190597534},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.19730892777442932},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.18346884846687317},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.1404179334640503},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.10049861669540405},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.09547629952430725},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"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/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.3390/e21050491","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e21050491","pdf_url":"https://www.mdpi.com/1099-4300/21/5/491/pdf?version=1558399768","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:33267205","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/33267205","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:doaj.org/article:734ed986240f444493afb52d535cdb72","is_oa":true,"landing_page_url":"https://doaj.org/article/734ed986240f444493afb52d535cdb72","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 5, p 491 (2019)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/1099-4300/21/5/491/","is_oa":true,"landing_page_url":"http://dx.doi.org/10.3390/e21050491","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:7514980","is_oa":true,"landing_page_url":"https://www.ncbi.nlm.nih.gov/pmc/articles/7514980","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/e21050491","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e21050491","pdf_url":"https://www.mdpi.com/1099-4300/21/5/491/pdf?version=1558399768","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":[],"awards":[{"id":"https://openalex.org/G6401056344","display_name":null,"funder_award_id":"71872110","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2946148876.pdf","grobid_xml":"https://content.openalex.org/works/W2946148876.grobid-xml"},"referenced_works_count":38,"referenced_works":["https://openalex.org/W1495058637","https://openalex.org/W1566211337","https://openalex.org/W1965024868","https://openalex.org/W1965580822","https://openalex.org/W1977043471","https://openalex.org/W2008369960","https://openalex.org/W2012587101","https://openalex.org/W2015816375","https://openalex.org/W2017205271","https://openalex.org/W2019950953","https://openalex.org/W2055151934","https://openalex.org/W2069134058","https://openalex.org/W2089041638","https://openalex.org/W2117802620","https://openalex.org/W2128530362","https://openalex.org/W2131202053","https://openalex.org/W2145479420","https://openalex.org/W2148880811","https://openalex.org/W2154589806","https://openalex.org/W2157791744","https://openalex.org/W2319520740","https://openalex.org/W2345954292","https://openalex.org/W2553445305","https://openalex.org/W2589789035","https://openalex.org/W2604351630","https://openalex.org/W2608945703","https://openalex.org/W2767074461","https://openalex.org/W2769275983","https://openalex.org/W2789592307","https://openalex.org/W2912189486","https://openalex.org/W2912565176","https://openalex.org/W2938041225","https://openalex.org/W3000565563","https://openalex.org/W3123979261","https://openalex.org/W4211007335","https://openalex.org/W6633996426","https://openalex.org/W6677304401","https://openalex.org/W6807091881"],"related_works":["https://openalex.org/W2380305602","https://openalex.org/W1024407309","https://openalex.org/W618881031","https://openalex.org/W3111454348","https://openalex.org/W4287554016","https://openalex.org/W2010778123","https://openalex.org/W3142142054","https://openalex.org/W2078547130","https://openalex.org/W1825854501","https://openalex.org/W2963256270"],"abstract_inverted_index":{"In":[0],"this":[1,105],"paper,":[2],"we":[3,40],"study":[4],"the":[5,37,50,66,75,91,94,101,112,121,125],"portfolio":[6,30,45],"selection":[7,31,46],"problem":[8],"considering":[9],"transaction":[10],"costs":[11],"under":[12],"multiple":[13,29],"periods.":[14],"For":[15],"non-professional":[16],"investors,":[17],"it":[18],"is":[19,97,115],"a":[20,42],"critical":[21],"factor":[22],"to":[23,48,65,81,99,119,128],"choose":[24,120],"an":[25,86],"appropriate":[26,83],"model":[27,47,122],"among":[28],"models":[32,127],"in":[33],"investment.":[34],"Based":[35],"on":[36,62,90],"credibility":[38],"measure,":[39],"formulate":[41],"multi-period":[43,106],"polynomial":[44,67],"gather":[49],"risk":[51,132],"indicators":[52,80],"involving":[53],"variance,":[54],"semi-variance,":[55],"entropy,":[56],"and":[57,123],"semi-entropy,":[58],"helping":[59],"investors":[60,72,118,129],"bet":[61],"assets.":[63],"According":[64],"goal":[68],"programming":[69],"(PGP)":[70],"approach,":[71],"can":[73],"conquer":[74],"fields":[76],"by":[77],"combining":[78],"apposite":[79],"build":[82],"models.":[84],"Subsequently,":[85],"adjusted":[87],"genetic":[88],"algorithm":[89],"foundation":[92],"of":[93,104],"penalty":[95],"function":[96],"designed":[98],"obtain":[100],"optimal":[102],"solution":[103],"model.":[107],"The":[108],"results":[109],"indicate":[110],"that":[111],"PGP":[113],"method":[114],"suitable":[116],"for":[117],"assigns":[124],"proper":[126],"with":[130],"different":[131],"preferences.":[133]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":2}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}