Worst-case risk with unspecified risk preferences

IF 1.9 2区 经济学 Q2 ECONOMICS Insurance Mathematics & Economics Pub Date : 2024-03-19 DOI:10.1016/j.insmatheco.2024.03.003
Haiyan Liu
{"title":"Worst-case risk with unspecified risk preferences","authors":"Haiyan Liu","doi":"10.1016/j.insmatheco.2024.03.003","DOIUrl":null,"url":null,"abstract":"<div><p>In this paper, we study the worst-case distortion risk measure for a given risk when information about distortion functions is partially available. We obtain the explicit forms of the worst-case distortion functions for several different sets of plausible distortion functions. When there is no concavity constraint on distortion functions, the worst-case distortion function is independent of the risk to be measured and the corresponding worst-case distortion risk measure is the weighted average of the VaR's of the risk for all decision makers. When the concavity constraint is imposed on distortion functions and the set of concave distortion functions is defined by the riskiness of one single risk, the explicit form of the worst-case distortion function is obtained, which depends the risk to be measured. When the set of concave distortion functions is defined by the riskiness of multiple risks, we reduce the infinite-dimensional optimization problem to a finite-dimensional optimization problem which can be solved numerically. Finally, we apply the worst-case risk measure to optimal decision making in reinsurance.</p></div>","PeriodicalId":54974,"journal":{"name":"Insurance Mathematics & Economics","volume":"116 ","pages":"Pages 235-248"},"PeriodicalIF":1.9000,"publicationDate":"2024-03-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Insurance Mathematics & Economics","FirstCategoryId":"96","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0167668724000386","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

Abstract

In this paper, we study the worst-case distortion risk measure for a given risk when information about distortion functions is partially available. We obtain the explicit forms of the worst-case distortion functions for several different sets of plausible distortion functions. When there is no concavity constraint on distortion functions, the worst-case distortion function is independent of the risk to be measured and the corresponding worst-case distortion risk measure is the weighted average of the VaR's of the risk for all decision makers. When the concavity constraint is imposed on distortion functions and the set of concave distortion functions is defined by the riskiness of one single risk, the explicit form of the worst-case distortion function is obtained, which depends the risk to be measured. When the set of concave distortion functions is defined by the riskiness of multiple risks, we reduce the infinite-dimensional optimization problem to a finite-dimensional optimization problem which can be solved numerically. Finally, we apply the worst-case risk measure to optimal decision making in reinsurance.

查看原文
分享 分享
微信好友 朋友圈 QQ好友 复制链接
本刊更多论文
未指定风险偏好的最坏情况风险
在本文中,我们研究了在变形函数信息部分可用的情况下,给定风险的最坏情况变形风险度量。我们获得了几组不同的可信失真函数的最坏情况失真函数的显式。当失真函数不存在凹凸约束时,最坏情况失真函数与要衡量的风险无关,相应的最坏情况失真风险度量是所有决策者的风险加权平均值。如果对失真函数施加凹约束,且凹失真函数集由单一风险的风险度定义,则可得到最坏情况失真函数的显式形式,该形式取决于待测风险。当凹畸变函数集由多种风险的风险度定义时,我们将无限维优化问题简化为有限维优化问题,该问题可以用数值方法求解。最后,我们将最坏情况风险度量应用于再保险的优化决策。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
求助全文
约1分钟内获得全文 去求助
来源期刊
Insurance Mathematics & Economics
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
90
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.
期刊最新文献
Evolution of institutional long-term care costs based on health factors Hidden semi-Markov models for rainfall-related insurance claims Continuous-time optimal reporting with full insurance under the mean-variance criterion A risk measurement approach from risk-averse stochastic optimization of score functions Distributionally robust insurance under the Wasserstein distance
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
现在去查看 取消
×
提示
确定
0
微信
客服QQ
Book学术公众号 扫码关注我们
反馈
×
意见反馈
请填写您的意见或建议
请填写您的手机或邮箱
已复制链接
已复制链接
快去分享给好友吧!
我知道了
×
扫码分享
扫码分享
Book学术官方微信
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术
文献互助 智能选刊 最新文献 互助须知 联系我们:info@booksci.cn
Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。
Copyright © 2023 Book学术 All rights reserved.
ghs 京公网安备 11010802042870号 京ICP备2023020795号-1