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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-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。
Reward and punishment system in the car insurance is very common. The thesis first introduces and discusses the optimal rewards and punishments system under the Poisson-Gamma hypothesis and its properties. Secondly, on the assumption that the claim frequency of individual policy obeys the binomial distribution and one parameter of the binomial distribution obeys Beta distribution, An optimal rewards and punishments system which takes into account the information of risk characteristics of individual policy, in which the risk characteristic information can be introduced into the rewards and punishments system through the generalized linear model. Then on the assumption that the claim frequency of individual policy obeys the negative binomial distribution and the negative binomial distribution One parameter obeys Beta distribution and establishes another optimal rewards and punishments system. Finally, the nature and application of these two reward and punishment systems are discussed.