论文标题
三个状态依赖性随机变量的总和的渐近学
Asymptotics for the sum of three state Markov dependent random variables
论文作者
论文摘要
当索赔金额取决于被保险人的状态（健康，生病或死亡）并在马尔可夫链中连接索赔时，保险模型就会被研究。在\ Mathbb {n} $周期中，签名的复合泊松近似值用于$ n \ in $ n \之后的汇总索赔分布。订单$ O（N^{ - 1}）$和$ O（N^{ - 1/2}）$的准确性分别为本地和统一规范获得。在特定情况下，总变化和非均匀估计的估计值至少属于$ o（n^{ - 1}）$的顺序。使用特征函数方法。结果可以应用于估计保险公司可能损失以优化保险费。
The insurance model when the amount of claims depends on the state of the insured person (healthy, ill, or dead) and claims are connected in a Markov chain is investigated. The signed compound Poisson approximation is applied to the aggregate claims distribution after $n\in \mathbb {N}$ periods. The accuracy of order $O(n^{-1})$ and $O(n^{-1/2})$ is obtained for the local and uniform norms, respectively. In a particular case, the accuracy of estimates in total variation and non-uniform estimates are shown to be at least of order $O(n^{-1})$. The characteristic function method is used. The results can be applied to estimate the probable loss of an insurer to optimize an insurance premium.
