离散更新风险模型中的最优投资与红利策略

在带有投资和红利支付的离散时间更新风险模型中,公司通过控制红利支付及风险投资和无风险投资的比例使股东破产前的累积贴现红利期望达到最大.本文通过分析HJB方程和变换值函数的方法得到了最优红利与投资策略的计算方法,并利用压缩映射和不动点原理证明了变换函数最优解的存在性.另外,为了显著降低计算量本文也创新地提出一种最优策略的随机模拟方法,并证明模拟结果是真实值的相合估计.最后使用Matlab软件利用随机模拟方法给出了一个数值计算实例,实例显示这种新的随机模拟方法是公司进行红利支付及投资决策的一个很好的可供参考的方法.

Optimal Investment and Dividend Strategy in the Discrete Sparre Andersen Risk Model

In the discrete-time Sparre Andersen risk model with investments and dividend payments,the company controls the dividend payments and the proportions of venture investments in order to maximize the cumulative expected discounted dividends prior to ruin.The paper gets the algorithm of the optimal dividend strategy by analyzing a Hamilton-Jacobi-Bellman equation and transforming the value function.Furthermore,the existence of the optimal solution of the transformation function is proved by using compression mapping and fixed point principle.In order to make the calculation easier,this paper also proposes an innovative random simulation method for the optimal strategy,and proves that the simulation result is the consistent estimate of the real value.Finally,the random simulation method in the Matlab is used for numerical analysis in an example,which shows the innovative simulation method is a very good and helpful method for making dividend payment and investment decisions.