Optimal reinsurance under VaR and TVaR risk measures in the presence of reinsurer’s risk limit

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• 作者：ZhiYi Lu^a ; ^{luzhiyi225@163.com" class="auth_mail" title="E-mail the corresponding author} ; LiLi Meng^a ; Yujin Wang^a ; Qingjie Shen^b
• 关键词：Optimal reinsurance ; Value-at-risk (VaR) ; Tail value-at-risk (TVaR) ; Risk limit ; Two-layer reinsurance ; Expectation premium principle
• 刊名：Insurance: Mathematics and Economics
• 出版年：2016
• 出版时间：May 2016
• 年：2016
• 卷：68
• 期：Complete
• 页码：92-100
• 全文大小：408 K

文摘

In most studies on optimal reinsurance, little attention has been paid to controlling the reinsurer’s risk. However, real-world insurance markets always place a limit on coverage, otherwise the insurer will be subjected to under a heavy financial burden when the insured suffers a large unexpected covered loss. In this paper, we revisit the optimal reinsurance problem under the optimality criteria of VaR and TVaR risk measures when the constraints for the reinsurer’s risk exposure are presented. Two types of constraints are considered that have been proposed by Cummins and Mahul (2004) and Zhou et al. (2010), respectively. It is shown that two-layer reinsurance is always the optimal reinsurance policy under both VaR and TVaR risk measures and under both types of constraints. This implies that the two-layer reinsurance policy is more robust. Furthermore, the optimal quantity of ceded risk depends on the confidence level, the safety loading and the tolerance level, as well as on the relation between them.