{"id":"https://openalex.org/W2790307039","doi":"https://doi.org/10.1155/2018/9180780","title":"On Minimizing the Ultimate Ruin Probability of an Insurer by Reinsurance","display_name":"On Minimizing the Ultimate Ruin Probability of an Insurer by Reinsurance","publication_year":2018,"publication_date":"2018-01-01","ids":{"openalex":"https://openalex.org/W2790307039","doi":"https://doi.org/10.1155/2018/9180780","mag":"2790307039"},"language":"en","primary_location":{"id":"doi:10.1155/2018/9180780","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2018/9180780","pdf_url":"http://downloads.hindawi.com/journals/jam/2018/9180780.pdf","source":{"id":"https://openalex.org/S190082376","display_name":"Journal of Applied Mathematics","issn_l":"1110-757X","issn":["1110-757X","1687-0042"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Applied Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"http://downloads.hindawi.com/journals/jam/2018/9180780.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5067689792","display_name":"Christian Kasumo","orcid":"https://orcid.org/0000-0002-5285-0846"},"institutions":[{"id":"https://openalex.org/I97231232","display_name":"Nelson Mandela African Institution of Science and Technology","ror":"https://ror.org/041vsn055","country_code":"TZ","type":"education","lineage":["https://openalex.org/I97231232"]}],"countries":["TZ"],"is_corresponding":true,"raw_author_name":"Christian Kasumo","raw_affiliation_strings":["Department of Applied Mathematics and Computational Science, Nelson Mandela African Institution of Science and Technology, P.O. Box 447, Arusha, Tanzania"],"raw_orcid":"https://orcid.org/0000-0002-5285-0846","affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics and Computational Science, Nelson Mandela African Institution of Science and Technology, P.O. Box 447, Arusha, Tanzania","institution_ids":["https://openalex.org/I97231232"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5043805790","display_name":"Juma Kasozi","orcid":"https://orcid.org/0000-0002-0941-9604"},"institutions":[{"id":"https://openalex.org/I72227227","display_name":"Makerere University","ror":"https://ror.org/03dmz0111","country_code":"UG","type":"education","lineage":["https://openalex.org/I72227227"]}],"countries":["UG"],"is_corresponding":false,"raw_author_name":"Juma Kasozi","raw_affiliation_strings":["Department of Mathematics, Makerere University, P.O. Box 7062, Kampala, Uganda"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Makerere University, P.O. Box 7062, Kampala, Uganda","institution_ids":["https://openalex.org/I72227227"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5069118419","display_name":"Dmitry Kuznetsov","orcid":"https://orcid.org/0000-0001-7177-0991"},"institutions":[{"id":"https://openalex.org/I97231232","display_name":"Nelson Mandela African Institution of Science and Technology","ror":"https://ror.org/041vsn055","country_code":"TZ","type":"education","lineage":["https://openalex.org/I97231232"]}],"countries":["TZ"],"is_corresponding":false,"raw_author_name":"Dmitry Kuznetsov","raw_affiliation_strings":["Department of Applied Mathematics and Computational Science, Nelson Mandela African Institution of Science and Technology, P.O. Box 447, Arusha, Tanzania"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics and Computational Science, Nelson Mandela African Institution of Science and Technology, P.O. Box 447, Arusha, Tanzania","institution_ids":["https://openalex.org/I97231232"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5067689792"],"corresponding_institution_ids":["https://openalex.org/I97231232"],"apc_list":{"value":1025,"currency":"USD","value_usd":1025},"apc_paid":{"value":1025,"currency":"USD","value_usd":1025},"fwci":1.9814,"has_fulltext":true,"cited_by_count":14,"citation_normalized_percentile":{"value":0.87070218,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"2018","issue":null,"first_page":"1","last_page":"11"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11720","display_name":"Probability and Risk Models","score":0.9998000264167786,"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":0.9998000264167786,"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/T12011","display_name":"Insurance, Mortality, Demography, Risk Management","score":0.9986000061035156,"subfield":{"id":"https://openalex.org/subfields/3317","display_name":"Demography"},"field":{"id":"https://openalex.org/fields/33","display_name":"Social 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":0.9955000281333923,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/reinsurance","display_name":"Reinsurance","score":0.9823618531227112},{"id":"https://openalex.org/keywords/hamilton\u2013jacobi\u2013bellman-equation","display_name":"Hamilton\u2013Jacobi\u2013Bellman equation","score":0.889971911907196},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6386411786079407},{"id":"https://openalex.org/keywords/block","display_name":"Block (permutation group theory)","score":0.5254917740821838},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5142230987548828},{"id":"https://openalex.org/keywords/diffusion","display_name":"Diffusion","score":0.45302388072013855},{"id":"https://openalex.org/keywords/volterra-integral-equation","display_name":"Volterra integral equation","score":0.4463990330696106},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.4440990388393402},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.2870925962924957},{"id":"https://openalex.org/keywords/integral-equation","display_name":"Integral equation","score":0.2819032669067383},{"id":"https://openalex.org/keywords/actuarial-science","display_name":"Actuarial science","score":0.2448137402534485},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.1927986741065979},{"id":"https://openalex.org/keywords/economics","display_name":"Economics","score":0.17005497217178345},{"id":"https://openalex.org/keywords/finance","display_name":"Finance","score":0.13024833798408508},{"id":"https://openalex.org/keywords/bellman-equation","display_name":"Bellman equation","score":0.07673731446266174},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.07320287823677063},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.07072094082832336}],"concepts":[{"id":"https://openalex.org/C166970017","wikidata":"https://www.wikidata.org/wiki/Q476118","display_name":"Reinsurance","level":2,"score":0.9823618531227112},{"id":"https://openalex.org/C196978813","wikidata":"https://www.wikidata.org/wiki/Q3302775","display_name":"Hamilton\u2013Jacobi\u2013Bellman equation","level":3,"score":0.889971911907196},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6386411786079407},{"id":"https://openalex.org/C2777210771","wikidata":"https://www.wikidata.org/wiki/Q4927124","display_name":"Block (permutation group theory)","level":2,"score":0.5254917740821838},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5142230987548828},{"id":"https://openalex.org/C69357855","wikidata":"https://www.wikidata.org/wiki/Q163214","display_name":"Diffusion","level":2,"score":0.45302388072013855},{"id":"https://openalex.org/C21965488","wikidata":"https://www.wikidata.org/wiki/Q2632613","display_name":"Volterra integral equation","level":3,"score":0.4463990330696106},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.4440990388393402},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.2870925962924957},{"id":"https://openalex.org/C27016315","wikidata":"https://www.wikidata.org/wiki/Q580101","display_name":"Integral equation","level":2,"score":0.2819032669067383},{"id":"https://openalex.org/C162118730","wikidata":"https://www.wikidata.org/wiki/Q1128453","display_name":"Actuarial science","level":1,"score":0.2448137402534485},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.1927986741065979},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.17005497217178345},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.13024833798408508},{"id":"https://openalex.org/C14646407","wikidata":"https://www.wikidata.org/wiki/Q1430750","display_name":"Bellman equation","level":2,"score":0.07673731446266174},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.07320287823677063},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.07072094082832336},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1155/2018/9180780","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2018/9180780","pdf_url":"http://downloads.hindawi.com/journals/jam/2018/9180780.pdf","source":{"id":"https://openalex.org/S190082376","display_name":"Journal of Applied Mathematics","issn_l":"1110-757X","issn":["1110-757X","1687-0042"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Applied Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:CULeuclid:euclid.jam/1521252013","is_oa":false,"landing_page_url":"https://projecteuclid.org/euclid.jam/1521252013","pdf_url":null,"source":{"id":"https://openalex.org/S4306400787","display_name":"Project Euclid (Cornell University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Text"},{"id":"pmh:oai:RePEc:hin:jnljam:9180780","is_oa":false,"landing_page_url":"http://downloads.hindawi.com/journals/JAM/2018/9180780.xml","pdf_url":null,"source":{"id":"https://openalex.org/S4306401271","display_name":"RePEc: Research Papers in Economics","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I77793887","host_organization_name":"Federal Reserve Bank of St. Louis","host_organization_lineage":["https://openalex.org/I77793887"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"},{"id":"pmh:oai:doaj.org/article:5e12387f4f0d4ecfb63407ebb6c33046","is_oa":true,"landing_page_url":"https://doaj.org/article/5e12387f4f0d4ecfb63407ebb6c33046","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":"Journal of Applied Mathematics, Vol 2018 (2018)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1155/2018/9180780","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2018/9180780","pdf_url":"http://downloads.hindawi.com/journals/jam/2018/9180780.pdf","source":{"id":"https://openalex.org/S190082376","display_name":"Journal of Applied Mathematics","issn_l":"1110-757X","issn":["1110-757X","1687-0042"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Applied Mathematics","raw_type":"journal-article"},"sustainable_development_goals":[{"score":0.6000000238418579,"id":"https://metadata.un.org/sdg/8","display_name":"Decent work and economic growth"}],"awards":[],"funders":[{"id":"https://openalex.org/F4320307857","display_name":"African Development Bank Group","ror":"https://ror.org/05gqz0k77"},{"id":"https://openalex.org/F4320326471","display_name":"Nelson Mandela African Institution of Science and Technology","ror":"https://ror.org/041vsn055"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2790307039.pdf","grobid_xml":"https://content.openalex.org/works/W2790307039.grobid-xml"},"referenced_works_count":14,"referenced_works":["https://openalex.org/W836612429","https://openalex.org/W1537137650","https://openalex.org/W1886569471","https://openalex.org/W1979653978","https://openalex.org/W2034085084","https://openalex.org/W2035925546","https://openalex.org/W2037007317","https://openalex.org/W2087292112","https://openalex.org/W2135955485","https://openalex.org/W2290309237","https://openalex.org/W2526287334","https://openalex.org/W2594978493","https://openalex.org/W3021895250","https://openalex.org/W3122431206"],"related_works":["https://openalex.org/W2180817123","https://openalex.org/W3171210036","https://openalex.org/W2380920362","https://openalex.org/W2376890406","https://openalex.org/W2349340733","https://openalex.org/W4306679469","https://openalex.org/W4312940986","https://openalex.org/W3038259942","https://openalex.org/W2355537005","https://openalex.org/W3121654678"],"abstract_inverted_index":{"We":[0,54],"consider":[1],"an":[2],"insurance":[3],"company":[4,18,103],"whose":[5],"reserves":[6],"dynamics":[7],"follow":[8],"a":[9,34,44],"diffusion-perturbed":[10,114],"risk":[11],"model.":[12],"To":[13],"reduce":[14],"its":[15],"risk,":[16],"the":[17,28,51,64,68,74,79,99,102,111],"chooses":[19],"to":[20,57],"reinsure":[21],"using":[22,63],"proportional":[23,96],"or":[24],"excess-of-loss":[25],"reinsurance.":[26],"Using":[27],"Hamilton-Jacobi-Bellman":[29],"(HJB)":[30],"approach,":[31],"we":[32,41],"derive":[33],"second-order":[35],"Volterra":[36,46],"integrodifferential":[37],"equation":[38,48],"(VIDE)":[39],"which":[40],"transform":[42],"into":[43],"linear":[45,60],"integral":[47],"(VIE)":[49],"of":[50,101],"second":[52],"kind.":[53],"then":[55],"proceed":[56],"solve":[58],"this":[59],"VIE":[61],"numerically":[62],"block-by-block":[65],"method":[66],"for":[67,78,110],"optimal":[69],"reinsurance":[70,97],"policy":[71],"that":[72,95],"minimizes":[73],"ultimate":[75],"ruin":[76],"probability":[77],"chosen":[80],"parameters.":[81],"Numerical":[82],"examples":[83],"with":[84],"both":[85,105],"light-":[86,106],"and":[87,107,113],"heavy-tailed":[88,108],"distributions":[89,109],"are":[90],"given.":[91],"The":[92],"results":[93],"show":[94],"increases":[98],"survival":[100],"in":[104],"Cram\u00e9r-Lundberg":[112],"models.":[115]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":4},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":4}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}