Optimal reinsurance with multivariate risks and dependence uncertainty

IF 6 2区 管理学 Q1 OPERATIONS RESEARCH & MANAGEMENT SCIENCE
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Abstract

In this paper, we study the optimal reinsurance design from the perspective of an insurer with multiple lines of business, where the reinsurance is purchased by the insurer for each line of business, respectively. For the risk vector generated by the multiple lines of business, we suppose that the marginal distributions are fixed, but the dependence structure between these risks is unknown. Due to the unknown dependence structure, the optimal strategy is investigated for the worst-case scenario. We consider two types of risk measures: Value-at-Risk (VaR) and Range-Value-at-Risk (RVaR) including Expected Shortfall (ES) as a special case, and general premium principles satisfying certain conditions. To be more practical, the minimization of the total risk is conducted under some budget constraint. For the VaR-based model with only two risks, it turns out that the limited stop-loss reinsurance treaty is optimal for each line of business. For the model with more than two risks, we obtain two types of optimal reinsurance strategies if the marginals have convex or concave distributions on their tail parts by constraining the ceded loss functions to be convex or concave. Moreover, as a special case, the optimal quota-share reinsurance with dependence uncertainty has been studied. Finally, after applying our findings to two risks, some studies have been implemented to obtain both the analytical and numerical optimal reinsurance policies.
具有多变量风险和依赖性不确定性的最优再保险
在本文中,我们从一家拥有多条业务线的保险公司的角度来研究最优再保险设计,即保险公司分别为每条业务线购买再保险。对于多条业务线产生的风险向量,我们假设边际分布是固定的,但这些风险之间的依赖结构是未知的。由于依赖结构未知,因此要研究最坏情况下的最优策略。我们考虑了两种风险度量:风险价值(VaR)和风险范围价值(RVaR),包括作为特例的预期缺口(ES),以及满足特定条件的一般溢价原则。为了更加实用,总风险最小化是在一定的预算约束下进行的。对于只有两种风险的基于 VaR 的模型,结果表明有限止损再保险条约对每种业务都是最优的。对于有两种以上风险的模型,如果边际值的尾部有凸或凹分布,我们可以通过约束分出损失函数为凸或凹,得到两种最优再保险策略。此外,作为一个特例,我们还研究了具有依赖性不确定性的最优配额分保再保险。最后,在将我们的研究结果应用于两种风险后,我们进行了一些研究,以获得分析和数值最优再保险政策。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
European Journal of Operational Research
European Journal of Operational Research 管理科学-运筹学与管理科学
CiteScore
11.90
自引率
9.40%
发文量
786
审稿时长
8.2 months
期刊介绍: The European Journal of Operational Research (EJOR) publishes high quality, original papers that contribute to the methodology of operational research (OR) and to the practice of decision making.
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