Time-consistent investment-reinsurance strategy for mean-variance insurers with a defaultable security

详细信息    查看全文

• 作者：Hui Zhao^a ; ^{zhaohuimath@tju.edu.cn" class="auth_mail" title="E-mail the corresponding author} ; Yang Shen^b ; ^{skyshen87@gmail.com" class="auth_mail" title="E-mail the corresponding author} ; Yan Zeng^c ; ^{zengy36@mail.sysu.edu.cn" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Defaultable bond ; Time-consistent strategy ; Investment and reinsurance ; Mean-variance criterion ; Insurer
• 刊名：Journal of Mathematical Analysis and Applications
• 出版年：2016
• 出版时间：15 May 2016
• 年：2016
• 卷：437
• 期：2
• 页码：1036-1057
• 全文大小：741 K

文摘

This paper considers an optimal investment and reinsurance problem involving a defaultable security for an insurer under the mean-variance criterion in a jump-diffusion risk model. The insurer can purchase proportional reinsurance or acquire new insurance business and invest in a financial market consisting of a risk-free asset, a stock and a defaultable bond. In particular, the correlation between the insurance risk model and the financial market is also considered. From a game theoretic perspective, the extended Hamilton–Jacobi–Bellman systems of equations are established for the post-default case and the pre-default case, respectively. In both cases, closed-form expressions for the optimal time-consistent investment-reinsurance strategies and the corresponding value functions are derived. Moreover, some properties of optimal strategies, value functions and efficient frontiers are discussed either analytically or numerically.