Research On Distribution Of Risk Parameter Within Each Level At Stationary State

With the economic development, the automotive industry has become one of the important pillar industries in China. The development of motor vehicle insurance has become inevitable at the same time. By now, there are nearly50companies of motor vehicle insurance in the market. Because of the market-oriented rate, the companies compete fiercely inevitably. In the current market, the PICC (Peoples Insurance Company of China), Ping An, CPIC (China Pacific Insurance Group Co., Ltd.) account for65%of the market. So that the rest of insurance companies wanted to occupy a place in the rest of the market, they certainly rush to take cheaper rate to attract customers. NCD (No Claim Discount) occupies a very important position in the motor vehicle insurance.Currently, the majority researches’on NCD system are basically on distribution of claims or amounts claimed, and then establish the optimal NCD system based on the assumed distribution.In the practice, the next year rate level is determined by the number of claims or the amounts claimed in this year. In the view of our application of NCD premium system soon, it is necessary to discussing NCD system in depth.However, the steady state is the most important aspect of NCD system, which determines the stability of company operation. In the past, it is really rough researching on steady state through probability matrix, which cannot explore the distribution of risk parameter within each level. At this point, this article derived the risk parameter distribution function by theoretical methods. However, the theoretical distribution is complicated and unpractical, so it is not desirable in practical applications. This paper presents a simulation method to simulate the real situation. Through the simulation method, the actual claims can be reproduced, the level can be transferred. According to the examination of internal risk parameter distribution, the NCD systems can be compared and improved. It is the focus of this article. In this article, NCD applications are based on the basis of risk heterogeneity. Following this assumption, the actual claims data is fitted. It is found that the risk parameters satisfy certain distribution. On this basis, the structure of risk parameters is researched follow steady state, which used the simulation idea. This paper is divided into six chapters.The first chapter is an introduction, including the research background, significance, contents of this article and the research methods and idea.NCD system model is introduced in Chapter2. The establishment of theoretical NCD model is discussed briefly in the first section. Whatever NCD system is built on, it is assumed that the claims obey a certain distribution. The common distribution and NCD systems are also summarized. In the second section, the NCD systems of PICC, Ping An and CPIC are showed, which are based on claims.The third chapter is the theoretical discussion of this article, which introduced the Markov process and stationary state. The existence of stationary state of practical NCD system is also proved. At last, the distribution of internal risk parameter in stationary state is derived. However, because of the distribution function is very complicated, it is necessary to find out the other idea to get the distribution of risk parameter in the stationary state.Chapter4presented the specific simulation ideas. Firstly, fitting the existing claims data is the important work. Therefore, in the first section, the fitting methods are introduced, such as MLE, the Chi-square test. Secondly, after tested with actual data, the Poisson inverse Gaussian distribution is selected, which is for the further analysis. Finally, based on the assumption of the claims that obey the Poisson inverse Gaussian distribution, it reaches the stationary state through simulation method and gets the statistics of each level risk parameter of PICC’s NCD system. According to the descriptive statistics results, the law of PICC’s NCD system is described, and the differences of stationary state between simulation and theory are explained.The NCD system of PICC, Ping an, CPIC, are compared in Chapter5, with using the simulation idea. Prior to this, few indicators which are usually used in evaluating NCD system are summarized. The common indicators of the three companies are calculated in the article. Then, followed by simulation method, the NCD systems are compared by descriptive statistics of the distribution of risk parameters. It is founded that CPIC’s NCD system is the most outstanding at distinguishing high risk policy, and Ping An’s NCD system is the best at considerably low risk policy.The simulation methods and practical value are discussed in Chapter6.According to mathematical modeling method, at first, this article estimates the distribution of risk parameter in stationary state, so that the theoretical study of NCD system is more in depth. Then this paper presents simulation method to show the internal risk parameters distribution, which is possible theoretical innovation in this paper. Through Matlab simulation procession, the stationary state has been achieved. For this simulation procession, the biggest value is that the stationary distribution can be more accurately estimated and the difference between different NCD systems in stationary state can be precisely compared.Although the conclusions of this paper are relatively simple, this paper presents a new way of thinking and solutions. It makes improvement in the evaluation of NCD system rather than calculating some simple indicators.