Optimal investment and dividend payment strategies with debt management and reinsurance
Optimal investment and dividend payment strategies with debt management and reinsurance
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债务管理和再保险的最佳投资和股息支付策略
DOI：
10.3934/jimo.2018009
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发表时间：
2018
影响因子：
1.3
通讯作者：
Wei Jiaqin
中科院分区：
文献类型：
--
作者：
Zhao Qian;Jin Zhuo;Wei Jiaqin
本文导出了某保险公司的最优负债率、投资和股利支付策略。盈余过程由再保险策略、债务水平、投资组合和意外冲击共同决定。目标是在三个控制变量的约束下，使有限时间内股利支付的总预期贴现效用最大化。效用函数选择为对数效用函数和幂效用函数。利用动态规划原理，该值函数是二阶非线性Hamilton-Jacobi-Bellman方程的解。导出了价值函数的显式解，得到了相应的最优负债率、投资和股利支付策略。此外，还考虑了投资借款约束、股利支付约束和再保险政策的影响，并分析了它们对最优策略的影响。进一步，为了考虑利率风险，在随机利率模型下对该问题进行了研究。
This paper derives the optimal debt ratio, investment and dividend payment strategies for an insurance company. The surplus process is jointly determined by the reinsurance strategies, debt levels, investment portfolios and unanticipated shocks. The objective is to maximize the total expected discounted utility of dividend payments in finite-time period subject to three control variables. The utility functions are chosen as the logarithmic and power utility functions. Using dynamic programming principle, the value function is the solution of a second-order nonlinear Hamilton-Jacobi-Bellman equation. The explicit solution of the value function is derived and the corresponding optimal debt ratio, investment and dividend payment strategies are obtained. In addition, the investment borrowing constraint, dividend payment constraint and impacts of reinsurance policies are considered and their impacts on the optimal strategies are analyzed. Further, to incorporating the interest rate risk, the problem is studied under a stochastic interest rate model.