最小化多重依赖风险下的惩罚性目标达成概率

IF 0.9 4区数学 Q3 STATISTICS & PROBABILITY

Statistics & Probability Letters Pub Date : 2024-10-24 DOI:10.1016/j.spl.2024.110287

Ying Huang, Jun Peng

{"title":"最小化多重依赖风险下的惩罚性目标达成概率","authors":"Ying Huang, Jun Peng","doi":"10.1016/j.spl.2024.110287","DOIUrl":null,"url":null,"abstract":"<div><div>We consider a robust optimal investment and reinsurance problem with multiple dependent risks for an Ambiguity-Averse Insurer (AAI), who wishes to minimize the probability that the value of the wealth process reaches a low barrier before a high goal. We assume that the insurer can purchase per-loss reinsurance for every class of insurance business and invest its surplus in a risk-free asset and a risky asset. Using the technique of stochastic control theory and solving the associated Hamilton-Jacobi-Bellman (HJB) equation, we derive the robust optimal investment-reinsurance strategy and the associated value function. We conclude that the robust optimal investment-reinsurance strategy coincides with the one without model ambiguity, but the value function differs. We also illustrate our results by numerical examples.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"217 ","pages":"Article 110287"},"PeriodicalIF":0.9000,"publicationDate":"2024-10-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Minimizing the penalized goal-reaching probability with multiple dependent risks\",\"authors\":\"Ying Huang, Jun Peng\",\"doi\":\"10.1016/j.spl.2024.110287\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><div>We consider a robust optimal investment and reinsurance problem with multiple dependent risks for an Ambiguity-Averse Insurer (AAI), who wishes to minimize the probability that the value of the wealth process reaches a low barrier before a high goal. We assume that the insurer can purchase per-loss reinsurance for every class of insurance business and invest its surplus in a risk-free asset and a risky asset. Using the technique of stochastic control theory and solving the associated Hamilton-Jacobi-Bellman (HJB) equation, we derive the robust optimal investment-reinsurance strategy and the associated value function. We conclude that the robust optimal investment-reinsurance strategy coincides with the one without model ambiguity, but the value function differs. We also illustrate our results by numerical examples.</div></div>\",\"PeriodicalId\":49475,\"journal\":{\"name\":\"Statistics & Probability Letters\",\"volume\":\"217 \",\"pages\":\"Article 110287\"},\"PeriodicalIF\":0.9000,\"publicationDate\":\"2024-10-24\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Statistics & Probability Letters\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0167715224002566\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"STATISTICS & PROBABILITY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Statistics & Probability Letters","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0167715224002566","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"STATISTICS & PROBABILITY","Score":null,"Total":0}

引用次数: 0

摘要

我们考虑的是模糊厌恶型保险公司（AAI）的稳健最优投资和再保险问题，该保险公司希望最大限度地降低财富过程的价值在达到高目标之前达到低障碍的概率。我们假设保险公司可以为每一类保险业务购买按损失再保险，并将盈余投资于无风险资产和风险资产。利用随机控制理论的技术并求解相关的汉密尔顿-雅各比-贝尔曼（HJB）方程，我们得出了稳健的最优投资-再保险策略和相关的价值函数。我们的结论是，稳健的最优投资-再保险策略与没有模型模糊性的策略相吻合，但价值函数不同。我们还通过数字示例来说明我们的结果。

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

Minimizing the penalized goal-reaching probability with multiple dependent risks

We consider a robust optimal investment and reinsurance problem with multiple dependent risks for an Ambiguity-Averse Insurer (AAI), who wishes to minimize the probability that the value of the wealth process reaches a low barrier before a high goal. We assume that the insurer can purchase per-loss reinsurance for every class of insurance business and invest its surplus in a risk-free asset and a risky asset. Using the technique of stochastic control theory and solving the associated Hamilton-Jacobi-Bellman (HJB) equation, we derive the robust optimal investment-reinsurance strategy and the associated value function. We conclude that the robust optimal investment-reinsurance strategy coincides with the one without model ambiguity, but the value function differs. We also illustrate our results by numerical examples.

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

Statistics & Probability Letters 数学-统计学与概率论

CiteScore

1.60

自引率

0.00%

发文量

173

审稿时长

6 months

期刊介绍： Statistics & Probability Letters adopts a novel and highly innovative approach to the publication of research findings in statistics and probability. It features concise articles, rapid publication and broad coverage of the statistics and probability literature. Statistics & Probability Letters is a refereed journal. Articles will be limited to six journal pages (13 double-space typed pages) including references and figures. Apart from the six-page limitation, originality, quality and clarity will be the criteria for choosing the material to be published in Statistics & Probability Letters. Every attempt will be made to provide the first review of a submitted manuscript within three months of submission. The proliferation of literature and long publication delays have made it difficult for researchers and practitioners to keep up with new developments outside of, or even within, their specialization. The aim of Statistics & Probability Letters is to help to alleviate this problem. Concise communications (letters) allow readers to quickly and easily digest large amounts of material and to stay up-to-date with developments in all areas of statistics and probability. The mainstream of Letters will focus on new statistical methods, theoretical results, and innovative applications of statistics and probability to other scientific disciplines. Key results and central ideas must be presented in a clear and concise manner. These results may be part of a larger study that the author will submit at a later time as a full length paper to SPL or to another journal. Theory and methodology may be published with proofs omitted, or only sketched, but only if sufficient support material is provided so that the findings can be verified. Empirical and computational results that are of significant value will be published.