{"id":"https://openalex.org/W4414548508","doi":"https://doi.org/10.1155/ijmm/7811845","title":"Modelling of Risk Process With Expense\u2010Augmented Loss Under Economic Factors and Its Application to Aggregated General Insurance Data in Kenya","display_name":"Modelling of Risk Process With Expense\u2010Augmented Loss Under Economic Factors and Its Application to Aggregated General Insurance Data in Kenya","publication_year":2025,"publication_date":"2025-01-01","ids":{"openalex":"https://openalex.org/W4414548508","doi":"https://doi.org/10.1155/ijmm/7811845"},"language":"en","primary_location":{"id":"doi:10.1155/ijmm/7811845","is_oa":true,"landing_page_url":"https://doi.org/10.1155/ijmm/7811845","pdf_url":"https://onlinelibrary.wiley.com/doi/pdfdirect/10.1155/ijmm/7811845","source":{"id":"https://openalex.org/S151851439","display_name":"International Journal of Mathematics and Mathematical Sciences","issn_l":"0161-1712","issn":["0161-1712","1687-0425"],"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":"International Journal of Mathematics and Mathematical Sciences","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://onlinelibrary.wiley.com/doi/pdfdirect/10.1155/ijmm/7811845","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5086054139","display_name":"Calvine Odiwuor","orcid":"https://orcid.org/0000-0002-8562-9734"},"institutions":[{"id":"https://openalex.org/I12859529","display_name":"University of Nairobi","ror":"https://ror.org/02y9nww90","country_code":"KE","type":"education","lineage":["https://openalex.org/I12859529"]}],"countries":["KE"],"is_corresponding":true,"raw_author_name":"Calvine Odiwuor","raw_affiliation_strings":["Department of Mathematics ,  University of Nairobi ,  Nairobi ,  Kenya , uonbi.ac.ke"],"raw_orcid":"https://orcid.org/0000-0002-8562-9734","affiliations":[{"raw_affiliation_string":"Department of Mathematics ,  University of Nairobi ,  Nairobi ,  Kenya , uonbi.ac.ke","institution_ids":["https://openalex.org/I12859529"]}]},{"author_position":"middle","author":{"id":null,"display_name":"Mwaniki Joseph","orcid":null},"institutions":[{"id":"https://openalex.org/I12859529","display_name":"University of Nairobi","ror":"https://ror.org/02y9nww90","country_code":"KE","type":"education","lineage":["https://openalex.org/I12859529"]}],"countries":["KE"],"is_corresponding":false,"raw_author_name":"Mwaniki Joseph","raw_affiliation_strings":["Department of Mathematics ,  University of Nairobi ,  Nairobi ,  Kenya , uonbi.ac.ke"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics ,  University of Nairobi ,  Nairobi ,  Kenya , uonbi.ac.ke","institution_ids":["https://openalex.org/I12859529"]}]},{"author_position":"middle","author":{"id":null,"display_name":"Ngare Philip","orcid":null},"institutions":[{"id":"https://openalex.org/I12859529","display_name":"University of Nairobi","ror":"https://ror.org/02y9nww90","country_code":"KE","type":"education","lineage":["https://openalex.org/I12859529"]}],"countries":["KE"],"is_corresponding":false,"raw_author_name":"Ngare Philip","raw_affiliation_strings":["Department of Mathematics ,  University of Nairobi ,  Nairobi ,  Kenya , uonbi.ac.ke"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics ,  University of Nairobi ,  Nairobi ,  Kenya , uonbi.ac.ke","institution_ids":["https://openalex.org/I12859529"]}]},{"author_position":"last","author":{"id":null,"display_name":"Simwa Richard","orcid":null},"institutions":[{"id":"https://openalex.org/I2802891092","display_name":"Machakos University","ror":"https://ror.org/05eyrmk93","country_code":"KE","type":"education","lineage":["https://openalex.org/I2802891092"]},{"id":"https://openalex.org/I44288286","display_name":"Daystar University","ror":"https://ror.org/01qmtv077","country_code":"KE","type":"education","lineage":["https://openalex.org/I44288286"]}],"countries":["KE"],"is_corresponding":false,"raw_author_name":"Simwa Richard","raw_affiliation_strings":["Department of Science ,  Daystar University ,  Machakos ,  Kenya"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Science ,  Daystar University ,  Machakos ,  Kenya","institution_ids":["https://openalex.org/I44288286","https://openalex.org/I2802891092"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5086054139"],"corresponding_institution_ids":["https://openalex.org/I12859529"],"apc_list":{"value":1025,"currency":"USD","value_usd":1025},"apc_paid":{"value":1025,"currency":"USD","value_usd":1025},"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.3329671,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"2025","issue":"1","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12394","display_name":"Insurance and Financial Risk Management","score":0.9998999834060669,"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"}},"topics":[{"id":"https://openalex.org/T12394","display_name":"Insurance and Financial Risk Management","score":0.9998999834060669,"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/T12011","display_name":"Insurance, Mortality, Demography, Risk Management","score":0.9990000128746033,"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/T11720","display_name":"Probability and Risk Models","score":0.9889000058174133,"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/underwriting","display_name":"Underwriting","score":0.758899986743927},{"id":"https://openalex.org/keywords/portfolio","display_name":"Portfolio","score":0.5752999782562256},{"id":"https://openalex.org/keywords/insurance-policy","display_name":"Insurance policy","score":0.43149998784065247},{"id":"https://openalex.org/keywords/risk-model","display_name":"Risk model","score":0.42320001125335693},{"id":"https://openalex.org/keywords/process","display_name":"Process (computing)","score":0.41670000553131104},{"id":"https://openalex.org/keywords/government","display_name":"Government (linguistics)","score":0.39989998936653137},{"id":"https://openalex.org/keywords/carry","display_name":"Carry (investment)","score":0.3384000062942505}],"concepts":[{"id":"https://openalex.org/C26503482","wikidata":"https://www.wikidata.org/wiki/Q1898080","display_name":"Underwriting","level":2,"score":0.758899986743927},{"id":"https://openalex.org/C162118730","wikidata":"https://www.wikidata.org/wiki/Q1128453","display_name":"Actuarial science","level":1,"score":0.6467999815940857},{"id":"https://openalex.org/C2780821815","wikidata":"https://www.wikidata.org/wiki/Q5340806","display_name":"Portfolio","level":2,"score":0.5752999782562256},{"id":"https://openalex.org/C149782125","wikidata":"https://www.wikidata.org/wiki/Q160039","display_name":"Econometrics","level":1,"score":0.43790000677108765},{"id":"https://openalex.org/C68799949","wikidata":"https://www.wikidata.org/wiki/Q977871","display_name":"Insurance policy","level":2,"score":0.43149998784065247},{"id":"https://openalex.org/C2986432223","wikidata":"https://www.wikidata.org/wiki/Q5449740","display_name":"Risk model","level":2,"score":0.42320001125335693},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.41749998927116394},{"id":"https://openalex.org/C98045186","wikidata":"https://www.wikidata.org/wiki/Q205663","display_name":"Process (computing)","level":2,"score":0.41670000553131104},{"id":"https://openalex.org/C2778137410","wikidata":"https://www.wikidata.org/wiki/Q2732820","display_name":"Government (linguistics)","level":2,"score":0.39989998936653137},{"id":"https://openalex.org/C2776299755","wikidata":"https://www.wikidata.org/wiki/Q432449","display_name":"Carry (investment)","level":2,"score":0.3384000062942505},{"id":"https://openalex.org/C127491075","wikidata":"https://www.wikidata.org/wiki/Q7617825","display_name":"Stochastic modelling","level":2,"score":0.31610000133514404},{"id":"https://openalex.org/C14293393","wikidata":"https://www.wikidata.org/wiki/Q2663825","display_name":"General insurance","level":3,"score":0.30720001459121704},{"id":"https://openalex.org/C144133560","wikidata":"https://www.wikidata.org/wiki/Q4830453","display_name":"Business","level":0,"score":0.3068000078201294},{"id":"https://openalex.org/C32896092","wikidata":"https://www.wikidata.org/wiki/Q189447","display_name":"Risk management","level":2,"score":0.2944999933242798},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.29249998927116394},{"id":"https://openalex.org/C29513703","wikidata":"https://www.wikidata.org/wiki/Q6398174","display_name":"Key person insurance","level":3,"score":0.28529998660087585},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.2752000093460083},{"id":"https://openalex.org/C145097563","wikidata":"https://www.wikidata.org/wiki/Q1148747","display_name":"Payment","level":2,"score":0.27230000495910645},{"id":"https://openalex.org/C62172701","wikidata":"https://www.wikidata.org/wiki/Q4826138","display_name":"Auto insurance risk selection","level":4,"score":0.26759999990463257},{"id":"https://openalex.org/C2778215004","wikidata":"https://www.wikidata.org/wiki/Q1137437","display_name":"Solvency","level":3,"score":0.25859999656677246},{"id":"https://openalex.org/C117568660","wikidata":"https://www.wikidata.org/wiki/Q1650843","display_name":"Multinomial logistic regression","level":2,"score":0.25600001215934753}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1155/ijmm/7811845","is_oa":true,"landing_page_url":"https://doi.org/10.1155/ijmm/7811845","pdf_url":"https://onlinelibrary.wiley.com/doi/pdfdirect/10.1155/ijmm/7811845","source":{"id":"https://openalex.org/S151851439","display_name":"International Journal of Mathematics and Mathematical Sciences","issn_l":"0161-1712","issn":["0161-1712","1687-0425"],"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":"International Journal of Mathematics and Mathematical Sciences","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:19105deb5cca408f9dc5d62912a2422a","is_oa":true,"landing_page_url":"https://doaj.org/article/19105deb5cca408f9dc5d62912a2422a","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":"International Journal of Mathematics and Mathematical Sciences, Vol 2025 (2025)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1155/ijmm/7811845","is_oa":true,"landing_page_url":"https://doi.org/10.1155/ijmm/7811845","pdf_url":"https://onlinelibrary.wiley.com/doi/pdfdirect/10.1155/ijmm/7811845","source":{"id":"https://openalex.org/S151851439","display_name":"International Journal of Mathematics and Mathematical Sciences","issn_l":"0161-1712","issn":["0161-1712","1687-0425"],"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":"International Journal of Mathematics and Mathematical Sciences","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4414548508.pdf","grobid_xml":"https://content.openalex.org/works/W4414548508.grobid-xml"},"referenced_works_count":43,"referenced_works":["https://openalex.org/W1540311291","https://openalex.org/W1967740507","https://openalex.org/W1977023568","https://openalex.org/W1979334596","https://openalex.org/W1980196592","https://openalex.org/W1981137970","https://openalex.org/W1998733805","https://openalex.org/W2007931305","https://openalex.org/W2008651998","https://openalex.org/W2011515496","https://openalex.org/W2040707473","https://openalex.org/W2044100216","https://openalex.org/W2055390972","https://openalex.org/W2062358551","https://openalex.org/W2063787873","https://openalex.org/W2080741384","https://openalex.org/W2081626699","https://openalex.org/W2082347486","https://openalex.org/W2084197669","https://openalex.org/W2084361475","https://openalex.org/W2084716442","https://openalex.org/W2095227476","https://openalex.org/W2101945349","https://openalex.org/W2136139078","https://openalex.org/W2149092492","https://openalex.org/W2162602207","https://openalex.org/W2182173776","https://openalex.org/W2303716823","https://openalex.org/W2326316747","https://openalex.org/W2485717584","https://openalex.org/W2765542298","https://openalex.org/W2905296953","https://openalex.org/W3022439851","https://openalex.org/W3025578174","https://openalex.org/W3121213441","https://openalex.org/W3123078594","https://openalex.org/W3123486469","https://openalex.org/W3125626638","https://openalex.org/W3155390747","https://openalex.org/W4229651066","https://openalex.org/W4232729308","https://openalex.org/W4245903884","https://openalex.org/W4289420647"],"related_works":[],"abstract_inverted_index":{"In":[0,21],"this":[1,248],"paper,":[2],"we":[3],"reformulate":[4],"the":[5,22,24,57,62,90,104,109,118,129,137,144,158,164,181,191,195,203,206,211,217,226,236,253,262,268],"classical":[6],"risk":[7,120,170,249],"model":[8,92,212],"to":[9,28,43,53,68,73,141,202,251,256],"consider":[10],"economic":[11,105,161],"factors":[12,162],"such":[13,107],"as":[14,95,108,166,188,272],"taxation":[15,115],"and":[16,61,70,84,114,223],"real":[17,110],"force":[18,111],"of":[19,56,112,136,147,160,183,190,205,210,221,261,270,275],"interest.":[20],"model,":[23,165,196],"premiums":[25],"are":[26,82,93,125],"assumed":[27],"be":[29,44,214],"compounded":[30],"by":[31],"increasing":[32],"annuities":[33],"over":[34],"some":[35],"time.":[36],"The":[37,87,132,168,208,239],"loss":[38,91,192],"process":[39,58,99,250],"is":[40,139,151,185,229],"also":[41,71,199],"presumed":[42],"two":[45],"mixed":[46],"stochastic":[47],"processes":[48],"with":[49,157,216],"weights":[50],"that":[51,153],"sum":[52],"1.":[54],"One":[55],"models":[59,171],"claims":[60],"other":[63,169,244],"model\u2019s":[64],"expenses":[65,81,184,198],"(expenses":[66],"due":[67,72],"underwriting":[69],"investments)":[74],"incurred":[75],"in":[76,89,117,143,163],"an":[77,258],"insurance":[78,119,233,254],"company.":[79],"These":[80],"long\u2010tailed":[83],"positively":[85],"skewed.":[86],"counts":[88],"modeled":[94],"a":[96,273],"dynamic":[97],"Heston":[98],"which":[100],"takes":[101],"into":[102],"consideration":[103],"factors,":[106],"interest":[113],"inherent":[116],"reserve":[121,204],"process.":[122],"Ruin":[123],"probabilities":[124,155],"hence":[126,265],"estimated":[127],"from":[128,230],"Lundberg":[130],"coefficient.":[131],"exact":[133],"closed":[134],"form":[135],"coefficient":[138],"obtained":[140,228],"help":[142,252],"graphical":[145],"approximation":[146,260],"ruin":[148,154,178,271],"probabilities.":[149],"It":[150],"observed":[152],"increase":[156],"inclusion":[159],"anticipated.":[167],"used":[172],"for":[173,235],"comparison":[174],"produce":[175],"significantly":[176],"lower":[177],"probabilities,":[179],"since":[180,225],"aspect":[182],"not":[186],"included":[187],"part":[189],"while":[193],"applying":[194],"yet":[197],"contribute":[200],"negatively":[201],"portfolio.":[207],"result":[209,274],"can":[213,246],"adopted":[215],"Insurance":[218],"Regulatory":[219],"Authority":[220],"Kenya":[222],"globally,":[224],"data":[227],"all":[231],"general":[232],"businesses":[234],"stated":[237],"period.":[238],"Kenyan":[240],"government":[241],"or":[242],"any":[243],"country":[245],"adopt":[247],"portfolio":[255],"have":[257],"accurate":[259],"financial":[263],"positions,":[264],"guarding":[266],"against":[267],"possibility":[269],"inaccurate":[276],"estimation.":[277]},"counts_by_year":[],"updated_date":"2026-06-14T06:11:07.267592","created_date":"2025-10-10T00:00:00"}