{"title":"无损失保费","authors":"Michael Fackler","doi":"10.1007/s13385-021-00302-0","DOIUrl":null,"url":null,"abstract":"<p>In insurance and even more in reinsurance it occurs that about a risk you only know that it has suffered no losses in the past, e.g. seven years. Some of these risks are furthermore such particular or novel that there are no similar risks to infer the loss frequency from. In this paper we propose a loss frequency estimator that copes with such situations, by just relying on the information coming from the risk itself: the “amended sample mean”. It is derived from a number of practice-oriented first principles and turns out to have desirable statistical properties. Some variants are possible, enabling insurers to align the method to their preferred business strategy, by trading off between low initial premiums for new business and moderate premium increases after a loss for renewal business. We further give examples where it is possible to assess the average loss from some market or portfolio information, such that overall one has an estimator of the risk premium.</p>","PeriodicalId":44305,"journal":{"name":"European Actuarial Journal","volume":null,"pages":null},"PeriodicalIF":0.8000,"publicationDate":"2022-01-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"Premium rating without losses\",\"authors\":\"Michael Fackler\",\"doi\":\"10.1007/s13385-021-00302-0\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>In insurance and even more in reinsurance it occurs that about a risk you only know that it has suffered no losses in the past, e.g. seven years. Some of these risks are furthermore such particular or novel that there are no similar risks to infer the loss frequency from. In this paper we propose a loss frequency estimator that copes with such situations, by just relying on the information coming from the risk itself: the “amended sample mean”. It is derived from a number of practice-oriented first principles and turns out to have desirable statistical properties. Some variants are possible, enabling insurers to align the method to their preferred business strategy, by trading off between low initial premiums for new business and moderate premium increases after a loss for renewal business. We further give examples where it is possible to assess the average loss from some market or portfolio information, such that overall one has an estimator of the risk premium.</p>\",\"PeriodicalId\":44305,\"journal\":{\"name\":\"European Actuarial Journal\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.8000,\"publicationDate\":\"2022-01-24\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"European Actuarial Journal\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1007/s13385-021-00302-0\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"BUSINESS, FINANCE\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"European Actuarial Journal","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1007/s13385-021-00302-0","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"BUSINESS, FINANCE","Score":null,"Total":0}
In insurance and even more in reinsurance it occurs that about a risk you only know that it has suffered no losses in the past, e.g. seven years. Some of these risks are furthermore such particular or novel that there are no similar risks to infer the loss frequency from. In this paper we propose a loss frequency estimator that copes with such situations, by just relying on the information coming from the risk itself: the “amended sample mean”. It is derived from a number of practice-oriented first principles and turns out to have desirable statistical properties. Some variants are possible, enabling insurers to align the method to their preferred business strategy, by trading off between low initial premiums for new business and moderate premium increases after a loss for renewal business. We further give examples where it is possible to assess the average loss from some market or portfolio information, such that overall one has an estimator of the risk premium.
期刊介绍：
Actuarial science and actuarial finance deal with the study, modeling and managing of insurance and related financial risks for which stochastic models and statistical methods are available. Topics include classical actuarial mathematics such as life and non-life insurance, pension funds, reinsurance, and also more recent areas of interest such as risk management, asset-and-liability management, solvency, catastrophe modeling, systematic changes in risk parameters, longevity, etc. EAJ is designed for the promotion and development of actuarial science and actuarial finance. For this, we publish original actuarial research papers, either theoretical or applied, with innovative applications, as well as case studies on the evaluation and implementation of new mathematical methods in insurance and actuarial finance. We also welcome survey papers on topics of recent interest in the field. EAJ is the successor of six national actuarial journals, and particularly focuses on links between actuarial theory and practice. In order to serve as a platform for this exchange, we also welcome discussions (typically from practitioners, with a length of 1-3 pages) on published papers that highlight the application aspects of the discussed paper. Such discussions can also suggest modifications of the studied problem which are of particular interest to actuarial practice. Thus, they can serve as motivation for further studies.Finally, EAJ now also publishes ‘Letters’, which are short papers (up to 5 pages) that have academic and/or practical relevance and consist of e.g. an interesting idea, insight, clarification or observation of a cross-connection that deserves publication, but is shorter than a usual research article. A detailed description or proposition of a new relevant research question, short but curious mathematical results that deserve the attention of the actuarial community as well as novel applications of mathematical and actuarial concepts are equally welcome. Letter submissions will be reviewed within 6 weeks, so that they provide an opportunity to get good and pertinent ideas published quickly, while the same refereeing standards as for other submissions apply. Both academics and practitioners are encouraged to contribute to this new format. Authors are invited to submit their papers online via http://euaj.edmgr.com.
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