{"id":"https://openalex.org/W1946583144","doi":"https://doi.org/10.1111/j.1539-6975.2012.01501.x","title":"Risk\u2010Minimizing Reinsurance Protection For Multivariate Risks","display_name":"Risk\u2010Minimizing Reinsurance Protection For Multivariate Risks","publication_year":2013,"publication_date":"2013-02-14","ids":{"openalex":"https://openalex.org/W1946583144","doi":"https://doi.org/10.1111/j.1539-6975.2012.01501.x","mag":"1946583144"},"language":"en","primary_location":{"id":"doi:10.1111/j.1539-6975.2012.01501.x","doi":"https://doi.org/10.1111/j.1539-6975.2012.01501.x","is_oa":false,"landing_page_url":"https://doi.org/10.1111/j.1539-6975.2012.01501.x","pdf_url":null,"source":{"id":"https://openalex.org/S116483603","display_name":"Journal of Risk & Insurance","issn_l":"0022-4367","issn":["0022-4367","1539-6975"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["abdc-a","anvur-class-a","anvur-scientific","cwts-core","fnege-2","jufo-2","norway-1","poland-140","russia-white-list-1","vabb-shw"],"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Risk and Insurance","raw_type":"journal-article"},"volume":null,"type":"article","is_traditional":true,"indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5108241561","display_name":"K.C. Cheung","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I177725633","display_name":"Chinese University of Hong Kong","ror":"https://ror.org/00t33hh48","country_code":"HK","type":"education","lineage":["https://openalex.org/I177725633"]},{"id":"https://openalex.org/I889458895","display_name":"University of Hong Kong","ror":"https://ror.org/02zhqgq86","country_code":"HK","type":"education","lineage":["https://openalex.org/I889458895"]}],"countries":["HK"],"is_corresponding":true,"raw_author_name":"K. C. Cheung","raw_affiliation_strings":["K. C. Cheung and K. C. J. Sung are at the Department of Statistics, and Actuarial Science, The University of Hong Kong, Pokfulam Road, Hong Kong. S. C. P. Yam is with the Department of Statistics, The Chinese University of Hong Kong, Shatin, N.T., Hong Kong. K. C. Cheung can be contacted via e-mail:","The University of Hong Kong, Department of Statistics and Actuarial Science"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"K. C. Cheung and K. C. J. Sung are at the Department of Statistics, and Actuarial Science, The University of Hong Kong, Pokfulam Road, Hong Kong. S. C. P. Yam is with the Department of Statistics, The Chinese University of Hong Kong, Shatin, N.T., Hong Kong. K. C. Cheung can be contacted via e-mail:","institution_ids":["https://openalex.org/I177725633","https://openalex.org/I889458895"]},{"raw_affiliation_string":"The University of Hong Kong, Department of Statistics and Actuarial Science","institution_ids":["https://openalex.org/I889458895"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5011650296","display_name":"K. C. J. Sung","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I177725633","display_name":"Chinese University of Hong Kong","ror":"https://ror.org/00t33hh48","country_code":"HK","type":"education","lineage":["https://openalex.org/I177725633"]},{"id":"https://openalex.org/I889458895","display_name":"University of Hong Kong","ror":"https://ror.org/02zhqgq86","country_code":"HK","type":"education","lineage":["https://openalex.org/I889458895"]}],"countries":["HK"],"is_corresponding":true,"raw_author_name":"K. C. J. Sung","raw_affiliation_strings":["K. C. Cheung and K. C. J. Sung are at the Department of Statistics, and Actuarial Science, The University of Hong Kong, Pokfulam Road, Hong Kong. S. C. P. Yam is with the Department of Statistics, The Chinese University of Hong Kong, Shatin, N.T., Hong Kong. K. C. Cheung can be contacted via e-mail:","The University of Hong Kong, Department of Statistics and Actuarial Science"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"K. C. Cheung and K. C. J. Sung are at the Department of Statistics, and Actuarial Science, The University of Hong Kong, Pokfulam Road, Hong Kong. S. C. P. Yam is with the Department of Statistics, The Chinese University of Hong Kong, Shatin, N.T., Hong Kong. K. C. Cheung can be contacted via e-mail:","institution_ids":["https://openalex.org/I177725633","https://openalex.org/I889458895"]},{"raw_affiliation_string":"The University of Hong Kong, Department of Statistics and Actuarial Science","institution_ids":["https://openalex.org/I889458895"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5075984844","display_name":"Sheung Chi Phillip Yam","orcid":"https://orcid.org/0000-0002-4380-0919","observed_orcids":["https://orcid.org/0000-0002-4380-0919"]},"institutions":[{"id":"https://openalex.org/I177725633","display_name":"Chinese University of Hong Kong","ror":"https://ror.org/00t33hh48","country_code":"HK","type":"education","lineage":["https://openalex.org/I177725633"]},{"id":"https://openalex.org/I889458895","display_name":"University of Hong Kong","ror":"https://ror.org/02zhqgq86","country_code":"HK","type":"education","lineage":["https://openalex.org/I889458895"]}],"countries":["HK"],"is_corresponding":true,"raw_author_name":"S. C. P. Yam","raw_affiliation_strings":["K. C. Cheung and K. C. J. Sung are at the Department of Statistics, and Actuarial Science, The University of Hong Kong, Pokfulam Road, Hong Kong. S. C. P. Yam is with the Department of Statistics, The Chinese University of Hong Kong, Shatin, N.T., Hong Kong. K. C. Cheung can be contacted via e-mail:","The Chinese University of Hong Kong Department of Statistics"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"K. C. Cheung and K. C. J. Sung are at the Department of Statistics, and Actuarial Science, The University of Hong Kong, Pokfulam Road, Hong Kong. S. C. P. Yam is with the Department of Statistics, The Chinese University of Hong Kong, Shatin, N.T., Hong Kong. K. C. Cheung can be contacted via e-mail:","institution_ids":["https://openalex.org/I177725633","https://openalex.org/I889458895"]},{"raw_affiliation_string":"The Chinese University of Hong Kong Department of Statistics","institution_ids":["https://openalex.org/I177725633"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5011650296","https://openalex.org/A5075984844","https://openalex.org/A5108241561"],"corresponding_institution_ids":["https://openalex.org/I177725633","https://openalex.org/I889458895"],"apc_list":{"value":3400,"currency":"USD","value_usd":3400},"apc_paid":null,"fwci":4.2595,"has_fulltext":false,"cited_by_count":28,"citation_normalized_percentile":{"value":0.93228703,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":88,"max":98},"biblio":{"volume":"81","issue":"1","first_page":"219","last_page":"236"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11720","display_name":"Probability and Risk Models","score":0.9775000214576721,"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/T11720","display_name":"Probability and Risk Models","score":0.9775000214576721,"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/T12394","display_name":"Insurance and Financial Risk Management","score":0.015300000086426735,"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":0.0052999998442828655,"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/optimal-reinsurance","display_name":"optimal reinsurance","score":0.9449999928474426},{"id":"https://openalex.org/keywords/multivariate-risk","display_name":"multivariate risk","score":0.8799999952316284},{"id":"https://openalex.org/keywords/min-max-optimization","display_name":"minimax optimization","score":0.7590000033378601},{"id":"https://openalex.org/keywords/stop-loss-reinsurance","display_name":"stop-loss reinsurance","score":0.9549999833106995},{"id":"https://openalex.org/keywords/minimax-theorem","display_name":"minimax theorem","score":0.7490000128746033}],"concepts":[{"id":"https://openalex.org/C166970017","wikidata":"https://www.wikidata.org/wiki/Q476118","display_name":"Reinsurance","level":2,"score":0.9069458842277527},{"id":"https://openalex.org/C149728462","wikidata":"https://www.wikidata.org/wiki/Q751319","display_name":"Minimax","level":2,"score":0.7956250905990601},{"id":"https://openalex.org/C161584116","wikidata":"https://www.wikidata.org/wiki/Q1952580","display_name":"Multivariate statistics","level":2,"score":0.6117501258850098},{"id":"https://openalex.org/C2781472820","wikidata":"https://www.wikidata.org/wiki/Q2154759","display_name":"Risk measure","level":3,"score":0.5953322052955627},{"id":"https://openalex.org/C144237770","wikidata":"https://www.wikidata.org/wiki/Q747534","display_name":"Mathematical economics","level":1,"score":0.46345752477645874},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.4619174003601074},{"id":"https://openalex.org/C2778757428","wikidata":"https://www.wikidata.org/wiki/Q1250464","display_name":"Realm","level":2,"score":0.42956048250198364},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4182712733745575},{"id":"https://openalex.org/C162118730","wikidata":"https://www.wikidata.org/wiki/Q1128453","display_name":"Actuarial science","level":1,"score":0.4153103232383728},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.41143345832824707},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.34321272373199463},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.3291236162185669},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.13023900985717773},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.12519627809524536},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.11085069179534912},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.07257005572319031},{"id":"https://openalex.org/C2780821815","wikidata":"https://www.wikidata.org/wiki/Q5340806","display_name":"Portfolio","level":2,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1111/j.1539-6975.2012.01501.x","doi":"https://doi.org/10.1111/j.1539-6975.2012.01501.x","is_oa":false,"landing_page_url":"https://doi.org/10.1111/j.1539-6975.2012.01501.x","pdf_url":null,"source":{"id":"https://openalex.org/S116483603","display_name":"Journal of Risk & Insurance","issn_l":"0022-4367","issn":["0022-4367","1539-6975"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["abdc-a","anvur-class-a","anvur-scientific","cwts-core","fnege-2","jufo-2","norway-1","poland-140","russia-white-list-1","vabb-shw"],"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Risk and Insurance","raw_type":"journal-article"},{"id":"pmh:oai:hub.hku.hk:10722/203424","doi":null,"is_oa":false,"landing_page_url":"http://hdl.handle.net/10722/203424","pdf_url":null,"source":{"id":"https://openalex.org/S4377196271","display_name":"The HKU Scholars Hub (University of Hong Kong)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I889458895","host_organization_name":"University of Hong Kong","host_organization_lineage":["https://openalex.org/I889458895"],"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"}],"best_oa_location":null,"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":44,"referenced_works":["https://openalex.org/W186520755","https://openalex.org/W588543767","https://openalex.org/W612335159","https://openalex.org/W1482237821","https://openalex.org/W1539941517","https://openalex.org/W1553648478","https://openalex.org/W1575356971","https://openalex.org/W1591570634","https://openalex.org/W1655713731","https://openalex.org/W1964809385","https://openalex.org/W1965593308","https://openalex.org/W1969765110","https://openalex.org/W1969897341","https://openalex.org/W1973012610","https://openalex.org/W1999645966","https://openalex.org/W2005173964","https://openalex.org/W2019291268","https://openalex.org/W2046396733","https://openalex.org/W2051444274","https://openalex.org/W2067009897","https://openalex.org/W2080381237","https://openalex.org/W2085749436","https://openalex.org/W2087540931","https://openalex.org/W2091213282","https://openalex.org/W2092698606","https://openalex.org/W2117723618","https://openalex.org/W2132527237","https://openalex.org/W2165923723","https://openalex.org/W2167264394","https://openalex.org/W2252980504","https://openalex.org/W2489822048","https://openalex.org/W2491670438","https://openalex.org/W2578992305","https://openalex.org/W3035509303","https://openalex.org/W3121841769","https://openalex.org/W3122576678","https://openalex.org/W3122717349","https://openalex.org/W3123946705","https://openalex.org/W3124407081","https://openalex.org/W3124740411","https://openalex.org/W4229984434","https://openalex.org/W4242439180","https://openalex.org/W4249667877","https://openalex.org/W6635523610"],"related_works":["https://openalex.org/W152115581","https://openalex.org/W4402857431","https://openalex.org/W2091213282","https://openalex.org/W2769807024","https://openalex.org/W1970743206","https://openalex.org/W2563220876","https://openalex.org/W7146956924","https://openalex.org/W2767072879","https://openalex.org/W7223021575","https://openalex.org/W2759563796"],"abstract_inverted_index":{"Abstract":[0],"In":[1,39],"this":[2],"article,":[3],"we":[4,61,79],"study":[5],"the":[6,19,28,37,47,63,71,84,90,102,118],"problem":[7],"of":[8,21,30,51,55,101,112],"optimal":[9,65,88,119],"reinsurance":[10,66],"policy":[11],"for":[12,116],"multivariate":[13],"risks":[14],"whose":[15],"quantitative":[16],"analysis":[17],"in":[18,36,69,89],"realm":[20],"general":[22,96],"law\u2010invariant":[23,97],"convex":[24,98],"risk":[25,99],"measures,":[26],"to":[27,45,81],"best":[29],"our":[31],"knowledge,":[32],"is":[33,42,75],"still":[34],"absent":[35],"literature.":[38],"reality,":[40],"it":[41],"often":[43],"difficult":[44],"determine":[46],"actual":[48],"dependence":[49,59],"structure":[50],"these":[52],"risks.":[53],"Instead":[54],"assuming":[56],"any":[57],"particular":[58],"structure,":[60],"propose":[62],"minimax":[64,108],"decision":[67],"formulation":[68],"which":[70],"worst":[72],"case":[73],"scenario":[74],"first":[76],"identified,":[77],"then":[78],"proceed":[80],"establish":[82],"that":[83,92],"stop\u2010loss":[85],"reinsurances":[86],"are":[87,121],"sense":[91],"they":[93],"minimize":[94],"a":[95],"measure":[100],"total":[103],"retained":[104],"risk.":[105],"By":[106],"using":[107],"theorem,":[109],"explicit":[110],"form":[111],"and":[113],"sufficient":[114],"condition":[115],"ordering":[117],"deductibles":[120],"also":[122],"obtained.":[123]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":3},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":5},{"year":2014,"cited_by_count":4}],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2016-06-24T00:00:00"}
