{"title":"鞅-等效混合复合泊松过程的表征","authors":"D. P. Lyberopoulos, N. D. Macheras","doi":"10.1214/20-AAP1604","DOIUrl":null,"url":null,"abstract":"If a given aggregate process S is a mixed compound Poisson process under a probability measure P , we provide a characterization of all probability measures Q on the domain of P , such that P and Q are progressively equivalent and S remains a mixed compound Poisson process with improved properties. This result generalizes earlier work of Delbaen & Haezendonck (1989). Implications related to the computation of premium calculation principles in an insurance market possessing the property of no free lunch with vanishing risk are also discussed.","PeriodicalId":50979,"journal":{"name":"Annals of Applied Probability","volume":"11 1","pages":""},"PeriodicalIF":2.2000,"publicationDate":"2021-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"A characterization of martingale-equivalent mixed compound Poisson processes\",\"authors\":\"D. P. Lyberopoulos, N. D. Macheras\",\"doi\":\"10.1214/20-AAP1604\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"If a given aggregate process S is a mixed compound Poisson process under a probability measure P , we provide a characterization of all probability measures Q on the domain of P , such that P and Q are progressively equivalent and S remains a mixed compound Poisson process with improved properties. This result generalizes earlier work of Delbaen & Haezendonck (1989). Implications related to the computation of premium calculation principles in an insurance market possessing the property of no free lunch with vanishing risk are also discussed.\",\"PeriodicalId\":50979,\"journal\":{\"name\":\"Annals of Applied Probability\",\"volume\":\"11 1\",\"pages\":\"\"},\"PeriodicalIF\":2.2000,\"publicationDate\":\"2021-04-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Annals of Applied Probability\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1214/20-AAP1604\",\"RegionNum\":2,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"STATISTICS & PROBABILITY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Annals of Applied Probability","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1214/20-AAP1604","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"STATISTICS & PROBABILITY","Score":null,"Total":0}
A characterization of martingale-equivalent mixed compound Poisson processes
If a given aggregate process S is a mixed compound Poisson process under a probability measure P , we provide a characterization of all probability measures Q on the domain of P , such that P and Q are progressively equivalent and S remains a mixed compound Poisson process with improved properties. This result generalizes earlier work of Delbaen & Haezendonck (1989). Implications related to the computation of premium calculation principles in an insurance market possessing the property of no free lunch with vanishing risk are also discussed.
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The Annals of Applied Probability aims to publish research of the highest quality reflecting the varied facets of contemporary Applied Probability. Primary emphasis is placed on importance and originality.
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