中文摘要：

奖惩系统在汽车保险中的应用非常普遍。论文首先介绍和讨论了泊松一伽马假设下的最优奖惩系统及其性质；其次在假设个体保单的索赔频率服从二项分布，而二项分布的一个参数服从贝塔分布的条件下，建立了一种考虑个体保单风险特征信息的最优奖惩系统，其中风险特征信息可以通过广义线性模型的形式引入奖惩系统；然后在假设个体保单的索赔频率服从负二项分布，而负二项分布的一个参数服从贝塔分布的条件下，建立了另一个最优奖惩系统；最后讨论了这两个奖惩系统的性质和应用。

英文摘要：

BMS is widely used in aotu insurance. The paper first discusses the optimal BMS and its properties under the Poisson-Gamma assumption. Then under the assumption that the claim frequency of a policyholder follows Binomial distribution and one parameter of the Binomial distribution is varying according to Beta distribution, the paper establishes an optimal bonus-malus system that can account for prior information of individual policies. The prior information can be introduced to the optimal bonus-malus system by generalized linear model. Under the assumption that the claim frequency of a policyholder follows Negative Binomial distribution and one parameter of the Negative Binomial is Beta distributed, another optimal bolus-malus system accounting for prior information of individual policies is established. The properties and applications of these optimal bonus-malus systems are also discussed.