{"id":"https://openalex.org/W2037159926","doi":"https://doi.org/10.1007/s00780-009-0104-1","title":"A generalization of Panjer\u2019s recursion and numerically stable risk aggregation","display_name":"A generalization of Panjer\u2019s recursion and numerically stable risk aggregation","publication_year":2009,"publication_date":"2009-08-19","ids":{"openalex":"https://openalex.org/W2037159926","doi":"https://doi.org/10.1007/s00780-009-0104-1","mag":"2037159926"},"language":"en","primary_location":{"id":"doi:10.1007/s00780-009-0104-1","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s00780-009-0104-1","pdf_url":null,"source":{"id":"https://openalex.org/S172526255","display_name":"Finance and Stochastics","issn_l":"0949-2984","issn":["0949-2984","1432-1122"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Finance and Stochastics","raw_type":"journal-article"},"type":"article","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/A5032284258","display_name":"Stefan Gerhold","orcid":"https://orcid.org/0000-0002-4172-3956"},"institutions":[{"id":"https://openalex.org/I145847075","display_name":"TU Wien","ror":"https://ror.org/04d836q62","country_code":"AT","type":"education","lineage":["https://openalex.org/I145847075"]}],"countries":["AT"],"is_corresponding":true,"raw_author_name":"Stefan Gerhold","raw_affiliation_strings":["Institute for Mathematical Methods in Economics, Vienna University of Technology, Wiedner Hauptstra\u00dfe 8\u201310/105-1, 1040, Vienna, Austria","Institute for Mathematical Methods in Economics, Vienna University of Technology, Vienna, Austria"],"affiliations":[{"raw_affiliation_string":"Institute for Mathematical Methods in Economics, Vienna University of Technology, Wiedner Hauptstra\u00dfe 8\u201310/105-1, 1040, Vienna, Austria","institution_ids":["https://openalex.org/I145847075"]},{"raw_affiliation_string":"Institute for Mathematical Methods in Economics, Vienna University of Technology, Vienna, Austria","institution_ids":["https://openalex.org/I145847075"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5001640960","display_name":"Uwe Schmock","orcid":"https://orcid.org/0000-0001-9588-8249"},"institutions":[{"id":"https://openalex.org/I145847075","display_name":"TU Wien","ror":"https://ror.org/04d836q62","country_code":"AT","type":"education","lineage":["https://openalex.org/I145847075"]}],"countries":["AT"],"is_corresponding":false,"raw_author_name":"Uwe Schmock","raw_affiliation_strings":["Institute for Mathematical Methods in Economics, Vienna University of Technology, Wiedner Hauptstra\u00dfe 8\u201310/105-1, 1040, Vienna, Austria","Institute for Mathematical Methods in Economics, Vienna University of Technology, Vienna, Austria"],"affiliations":[{"raw_affiliation_string":"Institute for Mathematical Methods in Economics, Vienna University of Technology, Wiedner Hauptstra\u00dfe 8\u201310/105-1, 1040, Vienna, Austria","institution_ids":["https://openalex.org/I145847075"]},{"raw_affiliation_string":"Institute for Mathematical Methods in Economics, Vienna University of Technology, Vienna, Austria","institution_ids":["https://openalex.org/I145847075"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5072030828","display_name":"Richard Warnung","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Richard Warnung","raw_affiliation_strings":["Risikomanagement, Raiffeisen Capital Management, Schwarzenbergplatz 3, 1010, Vienna, Austria","Risikomanagement, Raiffeisen Capital Management, Vienna, Austria"],"affiliations":[{"raw_affiliation_string":"Risikomanagement, Raiffeisen Capital Management, Schwarzenbergplatz 3, 1010, Vienna, Austria","institution_ids":[]},{"raw_affiliation_string":"Risikomanagement, Raiffeisen Capital Management, Vienna, Austria","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5032284258"],"corresponding_institution_ids":["https://openalex.org/I145847075"],"apc_list":{"value":2290,"currency":"EUR","value_usd":2890},"apc_paid":null,"fwci":2.1909,"has_fulltext":false,"cited_by_count":24,"citation_normalized_percentile":{"value":0.895584,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"14","issue":"1","first_page":"81","last_page":"128"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10282","display_name":"Financial Risk and Volatility Modeling","score":0.9991000294685364,"subfield":{"id":"https://openalex.org/subfields/2003","display_name":"Finance"},"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/T10282","display_name":"Financial Risk and Volatility Modeling","score":0.9991000294685364,"subfield":{"id":"https://openalex.org/subfields/2003","display_name":"Finance"},"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/T11720","display_name":"Probability and Risk Models","score":0.9987999796867371,"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/T10067","display_name":"Stochastic processes and financial applications","score":0.9983999729156494,"subfield":{"id":"https://openalex.org/subfields/2003","display_name":"Finance"},"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/recursion","display_name":"Recursion (computer science)","score":0.7987938523292542},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6146519780158997},{"id":"https://openalex.org/keywords/generalization","display_name":"Generalization","score":0.5897659659385681},{"id":"https://openalex.org/keywords/logarithm","display_name":"Logarithm","score":0.514358639717102},{"id":"https://openalex.org/keywords/exponent","display_name":"Exponent","score":0.5087175965309143},{"id":"https://openalex.org/keywords/distribution","display_name":"Distribution (mathematics)","score":0.5086796879768372},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5007519721984863},{"id":"https://openalex.org/keywords/poisson-distribution","display_name":"Poisson distribution","score":0.4839628040790558},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.47252991795539856},{"id":"https://openalex.org/keywords/negative-binomial-distribution","display_name":"Negative binomial distribution","score":0.4522545337677002},{"id":"https://openalex.org/keywords/mathematical-finance","display_name":"Mathematical finance","score":0.4374409317970276},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.38493382930755615},{"id":"https://openalex.org/keywords/mathematical-economics","display_name":"Mathematical economics","score":0.3267355263233185},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.23528075218200684},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.23133158683776855},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.1526312232017517},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.14481037855148315},{"id":"https://openalex.org/keywords/economics","display_name":"Economics","score":0.13730934262275696},{"id":"https://openalex.org/keywords/finance","display_name":"Finance","score":0.1111983060836792},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.10245490074157715}],"concepts":[{"id":"https://openalex.org/C168773036","wikidata":"https://www.wikidata.org/wiki/Q264164","display_name":"Recursion (computer science)","level":2,"score":0.7987938523292542},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6146519780158997},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.5897659659385681},{"id":"https://openalex.org/C39927690","wikidata":"https://www.wikidata.org/wiki/Q11197","display_name":"Logarithm","level":2,"score":0.514358639717102},{"id":"https://openalex.org/C2780388253","wikidata":"https://www.wikidata.org/wiki/Q5421508","display_name":"Exponent","level":2,"score":0.5087175965309143},{"id":"https://openalex.org/C110121322","wikidata":"https://www.wikidata.org/wiki/Q865811","display_name":"Distribution (mathematics)","level":2,"score":0.5086796879768372},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5007519721984863},{"id":"https://openalex.org/C100906024","wikidata":"https://www.wikidata.org/wiki/Q205692","display_name":"Poisson distribution","level":2,"score":0.4839628040790558},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.47252991795539856},{"id":"https://openalex.org/C199335787","wikidata":"https://www.wikidata.org/wiki/Q743364","display_name":"Negative binomial distribution","level":3,"score":0.4522545337677002},{"id":"https://openalex.org/C93373587","wikidata":"https://www.wikidata.org/wiki/Q335632","display_name":"Mathematical finance","level":2,"score":0.4374409317970276},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.38493382930755615},{"id":"https://openalex.org/C144237770","wikidata":"https://www.wikidata.org/wiki/Q747534","display_name":"Mathematical economics","level":1,"score":0.3267355263233185},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.23528075218200684},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.23133158683776855},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.1526312232017517},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.14481037855148315},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.13730934262275696},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.1111983060836792},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.10245490074157715},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1007/s00780-009-0104-1","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s00780-009-0104-1","pdf_url":null,"source":{"id":"https://openalex.org/S172526255","display_name":"Finance and Stochastics","issn_l":"0949-2984","issn":["0949-2984","1432-1122"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Finance and Stochastics","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.367.4302","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.367.4302","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.fam.tuwien.ac.at/~schmock/preprints/Stable_Panjer_Recursion.pdf","raw_type":"text"},{"id":"pmh:oai:RePEc:spr:finsto:v:14:y:2010:i:1:p:81-128","is_oa":false,"landing_page_url":"http://hdl.handle.net/10.1007/s00780-009-0104-1","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"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Decent work and economic growth","id":"https://metadata.un.org/sdg/8","score":0.6200000047683716}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":42,"referenced_works":["https://openalex.org/W85449395","https://openalex.org/W409616321","https://openalex.org/W592661564","https://openalex.org/W599484449","https://openalex.org/W623225750","https://openalex.org/W1538557949","https://openalex.org/W1542184596","https://openalex.org/W1548669759","https://openalex.org/W1592433032","https://openalex.org/W1965967625","https://openalex.org/W1982960058","https://openalex.org/W2017170340","https://openalex.org/W2022894179","https://openalex.org/W2031739262","https://openalex.org/W2044967912","https://openalex.org/W2055384294","https://openalex.org/W2069753003","https://openalex.org/W2084361475","https://openalex.org/W2085794632","https://openalex.org/W2098477731","https://openalex.org/W2108660885","https://openalex.org/W2116306732","https://openalex.org/W2119115519","https://openalex.org/W2126321713","https://openalex.org/W2130736678","https://openalex.org/W2140563563","https://openalex.org/W2140664056","https://openalex.org/W2156812602","https://openalex.org/W2318756145","https://openalex.org/W2325239405","https://openalex.org/W2399991609","https://openalex.org/W2468288461","https://openalex.org/W2488983277","https://openalex.org/W2547597265","https://openalex.org/W2751862591","https://openalex.org/W2797641211","https://openalex.org/W4243366103","https://openalex.org/W4285719527","https://openalex.org/W4292027056","https://openalex.org/W4299432846","https://openalex.org/W4301441647","https://openalex.org/W6617660898"],"related_works":["https://openalex.org/W1976679120","https://openalex.org/W4281614748","https://openalex.org/W2377519369","https://openalex.org/W30954630","https://openalex.org/W2765883196","https://openalex.org/W3202311233","https://openalex.org/W2034826746","https://openalex.org/W2396919090","https://openalex.org/W4389457771","https://openalex.org/W2042172774"],"abstract_inverted_index":null,"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":5},{"year":2014,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}