奖惩系统的数学建模与稳态分析  

THE MODELING AND EQUILIBRIUM ANALYSIS FOR BONUS-MALUS SYSTEMS

作　　者：伍宪彬[1] 

机构地区：[1]浙江万里学院基础学院,浙江宁波315010

出　　处：《经济数学》2005年第1期1-12,共12页Journal of Quantitative Economics

基　　金：国家自然科学基金资助项目 (No.199710 95 )

摘　　要：奖惩系统(Bonus- Malus Systems)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.本文在最一般的框架下,以有限齐次马尔科夫链对奖惩系统建模,证明了任一奖惩系统皆存在唯一的平稳分布,此外,给出了求解这一平稳分布的一般算法,并揭示了此平稳分布的结构.特别地,针对两种具有特定转移法则的奖惩系统,还给出了它们平稳分布的简明显式表示.Bonus-Malus System is an experience rating method, which is widely accepted in the automobile insurance markets all over the world. In this paper, the Bonus-Malus System is modeled by an finite homogeneous Markov chain in the most general framework. It is shown that, for any Bonus-Malus System, there always exists an unique stationary distribution. Besides, the general algorithm for determining this distribution is given and the structure of such stationary distribution is also shown. Particularly, for two kinds of Bonus-Malus System with special transition rules, the explicit formulas of corresponding stationary distribution are obtained.

关 键 词：奖惩系统 数学建模 马尔科夫链 平稳分布 保险数学 

分 类 号：F224.7[经济管理—国民经济] O211.62[理学—概率论与数理统计]