【摘要】 无索赔折扣系统(No Claim Discount system,简记为NCD系统)是世界各国机动车辆险中广泛采用的一种经验费率厘定机制.本文尝试建立了NCD系统严谨的数学理论, 重点讨论了NCD系统的数学建模和稳态分析.此外,作为本文必要的数学前提,首先在第2节着重探讨了随机矩阵间的随机优序关系,并将所得结论运用至齐次不可约且遍历的马尔科夫链的研究中,这些内容也有其独立的数学上的兴趣.更多还原

【Abstract】 No Claim Discount System (briefly denoted by NCD System) is an experience rating method which is widely accepted in the automobile insurance markets all over the world. we try to formulate its rigorous mathematical theory. Mainly, the mathemaical modeling and equilibrium analysis of NCD system will be shown in some details. As a necessary mathematical prerequisite for such discussions, in the second section, we first explore some properties of stochastic dominance order defined between stochastic matrices, and then apply the conclusions obtained to the researches of homogeneous, irreducible and ergodic Markov chain. Those contents have also their own mathematical interests too.更多还原