用概率方法处理保费率取决于水平的风险过程

IF 1.9 2区经济学 Q2 ECONOMICS

Insurance Mathematics & Economics Pub Date : 2024-06-26 DOI:10.1016/j.insmatheco.2024.06.002

Denis Denisov , Niklas Gotthardt , Dmitry Korshunov , Vitali Wachtel

{"title":"用概率方法处理保费率取决于水平的风险过程","authors":"Denis Denisov , Niklas Gotthardt , Dmitry Korshunov , Vitali Wachtel","doi":"10.1016/j.insmatheco.2024.06.002","DOIUrl":null,"url":null,"abstract":"<div><p>We study risk processes with level dependent premium rate. Assuming that the premium rate converges, as the risk reserve increases, to the critical value in the net-profit condition, we obtain upper and lower bounds for the ruin probability; our proving technique is purely probabilistic and based on the analysis of Markov chains with asymptotically zero drift.</p><p>We show that such risk processes give rise to heavy-tailed ruin probabilities whatever the distribution of the claim size, even if it is a bounded random variable. So, the risk processes with near critical premium rate provide an important example of a stochastic model where light-tailed input produces heavy-tailed output.</p></div>","PeriodicalId":54974,"journal":{"name":"Insurance Mathematics & Economics","volume":"118 ","pages":"Pages 142-156"},"PeriodicalIF":1.9000,"publicationDate":"2024-06-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0167668724000726/pdfft?md5=6232f72c323d396a7391ed63b243cb59&pid=1-s2.0-S0167668724000726-main.pdf","citationCount":"0","resultStr":"{\"title\":\"Probabilistic approach to risk processes with level-dependent premium rate\",\"authors\":\"Denis Denisov , Niklas Gotthardt , Dmitry Korshunov , Vitali Wachtel\",\"doi\":\"10.1016/j.insmatheco.2024.06.002\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>We study risk processes with level dependent premium rate. Assuming that the premium rate converges, as the risk reserve increases, to the critical value in the net-profit condition, we obtain upper and lower bounds for the ruin probability; our proving technique is purely probabilistic and based on the analysis of Markov chains with asymptotically zero drift.</p><p>We show that such risk processes give rise to heavy-tailed ruin probabilities whatever the distribution of the claim size, even if it is a bounded random variable. So, the risk processes with near critical premium rate provide an important example of a stochastic model where light-tailed input produces heavy-tailed output.</p></div>\",\"PeriodicalId\":54974,\"journal\":{\"name\":\"Insurance Mathematics & Economics\",\"volume\":\"118 \",\"pages\":\"Pages 142-156\"},\"PeriodicalIF\":1.9000,\"publicationDate\":\"2024-06-26\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://www.sciencedirect.com/science/article/pii/S0167668724000726/pdfft?md5=6232f72c323d396a7391ed63b243cb59&pid=1-s2.0-S0167668724000726-main.pdf\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Insurance Mathematics & Economics\",\"FirstCategoryId\":\"96\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0167668724000726\",\"RegionNum\":2,\"RegionCategory\":\"经济学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"ECONOMICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Insurance Mathematics & Economics","FirstCategoryId":"96","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0167668724000726","RegionNum":2,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"ECONOMICS","Score":null,"Total":0}

引用次数: 0

摘要

我们研究的是与保费率水平相关的风险过程。假设保费率随着风险准备金的增加而趋近于净利润条件下的临界值，我们就可以得到毁损概率的上下限；我们的证明技术纯粹是概率论的，基于对具有渐近零漂移的马尔可夫链的分析。我们的研究表明，无论索赔额的分布如何，这种风险过程都会产生重尾毁损概率，即使它是一个有界随机变量。因此，接近临界保费率的风险过程提供了一个重要的随机模型实例，即轻尾输入产生重尾输出。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

Probabilistic approach to risk processes with level-dependent premium rate

We study risk processes with level dependent premium rate. Assuming that the premium rate converges, as the risk reserve increases, to the critical value in the net-profit condition, we obtain upper and lower bounds for the ruin probability; our proving technique is purely probabilistic and based on the analysis of Markov chains with asymptotically zero drift.

We show that such risk processes give rise to heavy-tailed ruin probabilities whatever the distribution of the claim size, even if it is a bounded random variable. So, the risk processes with near critical premium rate provide an important example of a stochastic model where light-tailed input produces heavy-tailed output.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Insurance Mathematics & Economics 管理科学-数学跨学科应用

CiteScore

3.40

自引率

15.80%

发文量

审稿时长

17.3 weeks

期刊介绍： Insurance: Mathematics and Economics publishes leading research spanning all fields of actuarial science research. It appears six times per year and is the largest journal in actuarial science research around the world. Insurance: Mathematics and Economics is an international academic journal that aims to strengthen the communication between individuals and groups who develop and apply research results in actuarial science. The journal feels a particular obligation to facilitate closer cooperation between those who conduct research in insurance mathematics and quantitative insurance economics, and practicing actuaries who are interested in the implementation of the results. To this purpose, Insurance: Mathematics and Economics publishes high-quality articles of broad international interest, concerned with either the theory of insurance mathematics and quantitative insurance economics or the inventive application of it, including empirical or experimental results. Articles that combine several of these aspects are particularly considered.