{"id":"https://openalex.org/W2018644664","doi":"https://doi.org/10.1155/s1173912603000130","title":"Some results of ruin probability for the classical risk process","display_name":"Some results of ruin probability for the classical risk process","publication_year":2003,"publication_date":"2003-01-01","ids":{"openalex":"https://openalex.org/W2018644664","doi":"https://doi.org/10.1155/s1173912603000130","mag":"2018644664"},"language":"en","primary_location":{"id":"doi:10.1155/s1173912603000130","is_oa":true,"landing_page_url":"https://doi.org/10.1155/s1173912603000130","pdf_url":"https://downloads.hindawi.com/archive/2003/526402.pdf","source":{"id":"https://openalex.org/S187318915","display_name":"Journal of Applied Mathematics and Decision Sciences","issn_l":"1173-9126","issn":["1173-9126","1532-7612"],"is_oa":false,"is_in_doaj":false,"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 and Decision Sciences","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://downloads.hindawi.com/archive/2003/526402.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5071553240","display_name":"He Yuanjiang","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"He Yuanjiang","raw_affiliation_strings":["Department of Statistics Science, Zhongshan University, Ganglion, 510275 PR, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Statistics Science, Zhongshan University, Ganglion, 510275 PR, China","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5035388503","display_name":"Xucheng Li","orcid":"https://orcid.org/0000-0002-8081-2708"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Li Xucheng","raw_affiliation_strings":["Department of Statistics Science, Zhongshan University, Ganglion, 510275 PR, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Statistics Science, Zhongshan University, Ganglion, 510275 PR, China","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100342753","display_name":"John H. Zhang","orcid":"https://orcid.org/0000-0002-4319-4285"},"institutions":[{"id":"https://openalex.org/I200885203","display_name":"Indiana University of Pennsylvania","ror":"https://ror.org/0511cmw96","country_code":"US","type":"education","lineage":["https://openalex.org/I200885203"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"John Zhang","raw_affiliation_strings":["Department of Mathematics, Indiana University of Pennsylvania, Indiana, PA 15705, USA","Department of Mathematics, Indiana University of Pennsylvania, Indiana, PA, 15705, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Indiana University of Pennsylvania, Indiana, PA 15705, USA","institution_ids":["https://openalex.org/I200885203"]},{"raw_affiliation_string":"Department of Mathematics, Indiana University of Pennsylvania, Indiana, PA, 15705, USA","institution_ids":["https://openalex.org/I200885203"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":9,"citation_normalized_percentile":{"value":0.156555,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"7","issue":"3","first_page":"133","last_page":"146"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11720","display_name":"Probability and Risk Models","score":0.996399998664856,"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":0.996399998664856,"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/T11901","display_name":"Bayesian Methods and Mixture Models","score":0.98580002784729,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10968","display_name":"Statistical Distribution Estimation and Applications","score":0.9732999801635742,"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/algorithm","display_name":"Algorithm","score":0.5326777100563049},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.34046614170074463},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.3389216959476471}],"concepts":[{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5326777100563049},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.34046614170074463},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.3389216959476471}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1155/s1173912603000130","is_oa":true,"landing_page_url":"https://doi.org/10.1155/s1173912603000130","pdf_url":"https://downloads.hindawi.com/archive/2003/526402.pdf","source":{"id":"https://openalex.org/S187318915","display_name":"Journal of Applied Mathematics and Decision Sciences","issn_l":"1173-9126","issn":["1173-9126","1532-7612"],"is_oa":false,"is_in_doaj":false,"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 and Decision Sciences","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1155/s1173912603000130","is_oa":true,"landing_page_url":"https://doi.org/10.1155/s1173912603000130","pdf_url":"https://downloads.hindawi.com/archive/2003/526402.pdf","source":{"id":"https://openalex.org/S187318915","display_name":"Journal of Applied Mathematics and Decision Sciences","issn_l":"1173-9126","issn":["1173-9126","1532-7612"],"is_oa":false,"is_in_doaj":false,"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 and Decision Sciences","raw_type":"journal-article"},"sustainable_development_goals":[{"score":0.4699999988079071,"display_name":"Decent work and economic growth","id":"https://metadata.un.org/sdg/8"}],"awards":[],"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/W2018644664.pdf","grobid_xml":"https://content.openalex.org/works/W2018644664.grobid-xml"},"referenced_works_count":2,"referenced_works":["https://openalex.org/W1511170401","https://openalex.org/W1993495621"],"related_works":["https://openalex.org/W2748952813","https://openalex.org/W2051487156","https://openalex.org/W2073681303","https://openalex.org/W2390279801","https://openalex.org/W2358668433","https://openalex.org/W2376932109","https://openalex.org/W2001405890","https://openalex.org/W2382290278","https://openalex.org/W2478288626","https://openalex.org/W2350741829"],"abstract_inverted_index":{"The":[0],"computation":[1],"of":[2,20,46,133,199],"ruin":[3,37,85,131],"probability":[4,38,86,132],"is":[5,39,65,77,173,181,187,204],"an":[6],"important":[7],"problem":[8],"in":[9,17,70],"the":[10,18,50,55,59,62,71,74,84,89,93,99,130,134,138,142,197],"collective":[11],"risk":[12,52],"theory.":[13],"It":[14],"has":[15],"applications":[16],"fields":[19],"insurance,":[21],"actuarial":[22],"science,":[23],"and":[24,36,54,69,166,183],"economics.":[25],"Many":[26],"mathematical":[27],"models":[28,48],"have":[29],"been":[30],"introduced":[31],"to":[32],"simulate":[33],"business":[34],"activities":[35],"studied":[40,83],"based":[41,87],"on":[42,88],"these":[43,47],"models.":[44],"Two":[45],"are":[49],"classical":[51,60,90,135],"model":[53,91,136],"Cox":[56,72,79],"model.":[57],"In":[58],"model,":[61,73],"counting":[63,75],"process":[64,68,76],"a":[66,78,174,184],"Poisson":[67],"process.":[80],"Thorin":[81],"(1973)":[82],"with":[92,105,148],"assumption":[94],"that":[95],"random":[96,139],"sequence":[97,140],"followed":[98],"<mml:math":[100,108,118,123,143,151,157,162,167,190,200],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[101,109,119,124,144,152,158,163,168,191,201],"alttext=\"$\\Gamma$\"":[102,145],"id=\"E1\"><mml:mi>\u0393</mml:mi></mml:math>":[103],"distribution":[104,147],"density":[106,149],"function":[107,150],"alttext=\"$f(x)=\\frac{{x^{\\frac{1}{\\beta":[110],"}-":[111],"1}}}{{\\beta":[112],"^{\\frac{1}{\\beta":[113],"}}":[114],"\\Gamma({1/\\beta":[115],"})}}e^{-\\frac{x}{\\beta}}$\"":[116],"id=\"E2\"><mml:mi>f</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>x</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:mfrac><mml:mrow><mml:msup><mml:mi>x</mml:mi><mml:mrow><mml:mfrac><mml:mn>1</mml:mn><mml:mi>\u03b2</mml:mi></mml:mfrac><mml:mo>\u2212</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msup></mml:mrow><mml:mrow><mml:msup><mml:mi>\u03b2</mml:mi><mml:mrow><mml:mfrac><mml:mn>1</mml:mn><mml:mi>\u03b2</mml:mi></mml:mfrac></mml:mrow></mml:msup><mml:mi>\u0393</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mn>1</mml:mn><mml:mo>/</mml:mo><mml:mi>\u03b2</mml:mi></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:mfrac><mml:msup><mml:mi>e</mml:mi><mml:mrow><mml:mo>\u2212</mml:mo><mml:mfrac><mml:mi>x</mml:mi><mml:mi>\u03b2</mml:mi></mml:mfrac></mml:mrow></mml:msup></mml:math>,":[117],"alttext=\"$x&gt;0$\"":[120,159],"id=\"E3\"><mml:mi>x</mml:mi><mml:mo>&gt;</mml:mo><mml:mn>0</mml:mn></mml:math>,":[121],"where":[122,137,161],"alttext=\"$\\beta&gt;1$\"":[125],"id=\"E4\"><mml:mi>\u03b2</mml:mi><mml:mo>&gt;</mml:mo><mml:mn>1</mml:mn></mml:math>.":[126],"This":[127],"paper":[128],"studies":[129,195],"follows":[141],"id=\"E5\"><mml:mi>\u0393</mml:mi></mml:math>":[146],"alttext=\"$f(x)=\\frac{{\\alpha^n}}{{\\Gamma(n)}}x^{n-1}":[153],"e^{-\\alpha":[154],"x}$\"":[155],"id=\"E6\"><mml:mi>f</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>x</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:mfrac><mml:mrow><mml:msup><mml:mi>\u03b1</mml:mi><mml:mi>n</mml:mi></mml:msup></mml:mrow><mml:mrow><mml:mi>\u0393</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>n</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:mfrac><mml:msup><mml:mi>x</mml:mi><mml:mrow><mml:mi>n</mml:mi><mml:mo>\u2212</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msup><mml:msup><mml:mi>e</mml:mi><mml:mrow><mml:mo>\u2212</mml:mo><mml:mi>\u03b1</mml:mi><mml:mi>x</mml:mi></mml:mrow></mml:msup></mml:math>,":[156],"id=\"E7\"><mml:mi>x</mml:mi><mml:mo>&gt;</mml:mo><mml:mn>0</mml:mn></mml:math>,":[160],"alttext=\"$\\alpha&gt;0$\"":[164],"id=\"E8\"><mml:mi>\u03b1</mml:mi><mml:mo>&gt;</mml:mo><mml:mn>0</mml:mn></mml:math>":[165],"alttext=\"$n":[169],"\\geqslant":[170],"2$\"":[171],"id=\"E9\"><mml:mi>n</mml:mi><mml:mo>\u2265</mml:mo><mml:mn>2</mml:mn></mml:math>":[172],"positive":[175],"integer.":[176],"An":[177],"intermediate":[178],"general":[179],"result":[180],"given":[182],"complete":[185],"solution":[186],"provided":[188],"for":[189,196],"alttext=\"$n=2$\"":[192,202],"id=\"E10\"><mml:mi>n</mml:mi><mml:mo>=</mml:mo><mml:mn>2</mml:mn></mml:math>.":[193],"Simulation":[194],"case":[198],"id=\"E11\"><mml:mi>n</mml:mi><mml:mo>=</mml:mo><mml:mn>2</mml:mn></mml:math>":[203],"also":[205],"provided.":[206]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":1},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}
