Optimal investment and dividend for an insurer under a Markov regime switching market with high gain tax
Optimal investment and dividend for an insurer under a Markov regime switching market with high gain tax
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DOI：
10.3934/jimo.2018154
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发表时间：
2020
影响因子：
1.3
通讯作者：
Lin Xu;Dingjun Yao;Gong Cheng
中科院分区：
文献类型：
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作者：
Lin Xu;Dingjun Yao;Gong Cheng
本文研究了具有CRRA偏好的保险公司的最优投资和分红问题。保险人的目标是最大化破产前红利的期望折现累积效用，且支付高额利得税。盈余过程和金融市场都受到外部马尔可夫链的调节。利用弱动态规划原理（WDPP），证明了该控制问题的值函数是一阶导数约束的耦合Hamilton-Jacobi-Bellman（HJB）方程的唯一粘性解.通过求解一个不存在制度转换的辅助问题，证明了在多制度市场中，保险人采用与单制度市场相同的策略是最优的。证明了粘性解在其定义域上的正则性，从而证明了HJB方程存在经典解。利用马尔可夫链近似方法给出了价值函数的数值格式，并通过两个算例说明了高收益税和体制转换对最优策略的影响。
This study examines the optimal investment and dividend problem for an insurer with CRRA preference. The insurer's goal is to maximize the expected discounted accumulated utility from dividend before ruin and the insurer subjects to high gain tax payment. Both the surplus process and the financial market are modulated by an external Markov chain. Using the weak dynamic programming principle (WDPP), we prove that the value function of our control problem is the unique viscosity solution to coupled Hamilton-Jacobi-Bellman (HJB) equations with first derivative constraints. Solving an auxiliary problem without regime switching, we prove that, it is optimal for the insurer in a multiple-regime market to adopt the policies in the same way as in a single-regime market. The regularity of the viscosity solution on its domain is proved and thus the HJB equations admits classical solution. A numerical scheme for the value function is provided by the Markov chain approximation method, two numerical examples are given to illustrate the impact of the high gain tax and regime switching on the optimal policies.