Analysis of China Motor Vehicle Insurance Business Trends

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1 Analysis of China Motor Vehicle Insurance Business Trends 1 Xiaohui WU, 2 Zheng Zhang, 3 Lei Liu, 4 Lanlan Zhang 1, First Autho University of International Business and Economic, Beijing, *2,Corresponding Author Sinosoft co., LTD, 3,4 Beijing University of Technology Beijing , of Software of Chinese Academy of Sciences Beijing , Abstract After thirty years reform and opening, China has seen a rapid economic development. Along with the country's growing wealth and improved living conditions, citizens have growing awareness of the necessity of insurance, thus the insurance demands increased significantly and the industry has sustained rapid development for a long time. Along with the high accelerated developed of motor vehicle industry,. Motor vehicle insurance has taken 74.6% of total premium revenue of the property insurance industry in Prediction of motor vehicle insurance premiums has a significant impact on setting company goals and developing company business development plan in this situation. This paper predicts China's motor vehicle insurance premiums of next five years which can provide a theoretical basis for the 12th five year plan. According to the characteristics of motor vehicle insurance income, this paper adopted the improved gray forecast model to enhance forecast accuracy. Keywords: Economic Growth, Improved Gray Forecast Model, Premium Income Forecast 1. Introduction Since China's insurance industry gradually integrates into the international insurance market, the motor vehicle insurance market grows continually while the market becomes intensively competitive. Everyone knows that insurance premium income is an important indicator of the atmosphere of this industry, for example, it will reflect the development state and penetration level of the whole market, meanwhile for every company it is an important source of profits and an important guarantee to establish insurance funds and carry out insurance compensations. Consequently, all insurance companies count the premium plan as part of business development objectives and take it into consideration when making any business decisions. So the research and forecasting for the size of the premium is very important, for it is a significant basic for the development of the company's premium plan. Premium forecasting means making estimation for the possible premium growth. Premium prediction has several functions, first, it can help insurance companies to understand and control the uncertainty of the future in order to minimize the possible losses, so that we can get a broad view of the company's future development and trends; second, it will make the whole plan keep pace with the changing market environment and economic conditions. The premium forecast makes simulation prediction based on the data of several years and uses qualitative analysis method to estimate the insurance premium by controlling the economic, social conditions of the current and previous years; third, it will be helpful to get prior insight into the influences of some policy and make the appropriate decisions and responding strategies. For an organization, both making plans and decisions needs the basic of estimating the future conditions fundamentally. Arranging the business process and plans after that will ensures the stability along with enterprises development. It has a long history of premium prediction home and abroad, with the growth of the insurance industry, premium forecast model has become a hot topics and methods used has grown more mature. However, considering the diversity of the factors that will affect premium income and the complexity of forecast itself, our premium forecasts should base on the current situation here in China and make further exploration. In this paper, the gray prediction model based on gray system has been proposed, and the gray prediction model was improved by considering the characteristics of motor vehicle insurance Advances in information Sciences and Service Sciences(AISS) Volume3, Number11. December 2011 doi : /AISS.vol3.issue11.51

2 premiums and its sequence. The model can effectively improve the precision of premiums prediction. After that, the authors predicted the motor vehicle insurance premiums in next five years. 2. Prediction model of motor vehicle insurance premiums (1) Premium prediction model The development of insurance market is affected by many factors so the annual premium growth can not be expressed by a particular function. Since many factors that impact the motor vehicle insurance premium income are lack of data, the using of some traditional forecasting methods (such as linear regression, exponential curve regression model, exponential smoothing model, etc.) is restricted. Regression analysis is a method of forecasting variables based on the causal relationship between variables [1]. In prediction model, the premium was set as the explained variable. When selecting potential explanatory variables, only the main variables affecting in premiums are considered. This is the shortcomings of using regression analysis because we cannot take all the factors into account. Similarly, when applying BP artificial neural network prediction model [2], the prediction precision by studying the influence degree and relevancy of target variable factors was enhanced, however, it is too much trouble on impact factors selection, and inaccuracy and lack of data are the main reasons of training error. [3]. Gray prediction model can be applied in systems with incomplete and uncertain information. Predictive models are established on characteristic of data sequence and make effective supervision and correct description on the system behavior and evolution. It operates conveniently, easy-to-test and can get a satisfactory reliability result based on a small amount of data. It can be applied to the explosive exponential growth sequence. Gray prediction model can solve the problems of motor vehicle insurance premium forecast. Meanwhile the motor vehicle insurance premium income data sequence meets the gray model s requirements for time series. For reasons above, the gray prediction model are widely used to forecast the motor vehicle insurance premium for its practicality and convenience [4]. In the paper, the gray prediction model is used to predict the premium. (2) Traditional gray prediction model and its weakness [5] Gray prediction uses the time-series of prediction object itself as sample. Thus, it seems that the associated factor is not involved in computing and modeling. However, it doesn t mean those factors did not play a role in the prediction and this method will affect the comprehensiveness of the model. And this is why it is called gray. The motor vehicle insurance premium income data of previous years are time series of this model. The paper introduces traditional Gray prediction model from Xu Liang, Zhao Changli makes evaluation [6-9]. (0) (0) (0) (0) Time series of Gray forecasting model x [ x (1), x (2),, x ( n)] k (1) (0) The time series is summed x ( k) x ( i), i1, 2,3,, n. The simple adding cannot form a i1 good original random sequence and will impact on the accuracy of the model (1) (0) (1) (1) x ( k) x ( k) x ( k 1), dx (1) ax u dt This is a variable s first-order differential equations mark parameter column of GM (1,1) as â, a aˆ u T -1 T So by using the Least square method, solve aˆ ( B B) B Y N (1) Z (2)1 (1) (1) (1) (1) Z (3)1 B, Z ( k) ax ( k) [1 a] x ( k 1) (1) Z (4)1

3 a is set as 0.5. Selection of value of a is the shortage of traditional gray prediction model. Z (1) ( k ) is set as half value of the trapezoidal area. The correct value is the integral between x (1) ( k ) and x (1) ( k 1). The solution of differential equation is (1) (0) u ak u xˆ ( k1) [ x (1) ] e. The default setting is taking a a the first point of original sequence as the coincidence point. When fitting the graphics, the exact position of the coincidence point can t be decided. Inappropriate choice of coincidence point will make the similarity of the graphics fitting difficult. (0) (1) (1) Restore above equation, we get xˆ ( k) xˆ ( k) xˆ ( k 1). 3. Improved prediction model and premium model checking (1) Model and data description Gray prediction model has good forecasting accuracy for the short sequences, less volatile time series, while for the long-term forecasts especially for volatile time series, the prediction gets a poor accuracy. Only when the time series is close to discrete smooth index series, and the number of indexes is less, the gray prediction model can have a good accuracy. It often gets great lag error for highgrowth index series. In this paper, the time series of motor vehicle premiums is processed according to the characteristics of gray prediction model, to make it more in line with the requirements for time series for the gray prediction model, and then the forecast accuracy is improved. Based on the gray prediction model [9-11], this paper adopted the improved gray prediction model to make it more suitable for motor vehicle insurance premium forecast [10-12]. In this paper, we take three improvements aiming at the problems of traditional model: the first is smoothing the original sequence; the second is the construct method of the background value and the third is the choice of the initial value of the model. In addition, the original sequence length is determined based on the average relative error which is tested on the model according to the characteristics of the model. (0) (0) (0) (0) Determine the length of the time sequence series n, x [ x (1), x (2),, x ( n)] Process log or index change on the time series to make it closer to the smooth discrete sequences of mall index, and restore data in the final result; Calculate the background value (1) (1) (1) Z ( k) ax ( k) [1 a] x ( k 1), is set as 0.5 usually, but it is not appropriate to motor vehicle insurance premium income data series which has a rapid growth. So the value of is adjusted to match the trend of motor vehicle insurance premium income data series; In the traditional gray prediction model, it is not appropriate to consider x (1) (1) as a known condition. This paper sets its value according to the reality to improve the fitting and prediction accuracy. (1) (1) u a( km1) u X ( k 1) X ( m) e, m 1, 2,, n a q The time series in Figure 1 describe motor vehicle insurance premium income. As can be seen from the figure, the premium income experiences a higher growth rate from 2008 to 2010 than the previous years, and which indicates that motor vehicle insurance industry in China is developing rapidly in recent years, and that accords with the rapid development trend of our nation in recent years. Motor vehicle insurance premium forecast is noteworthy aspects because the living standard of national life and national development situation can be observed from it. [13]

4 Figure China auto insurance premium income premium growth rate in Figure 2. China's auto insurance Source: National Bureau of Statistics: China Statistical Yearbook, Beijing: China Statistics Press In figure 2, the China motor vehicle insurance premium income has a steady growth, but the strength of the growth is very different. For example, in 2010, because of the state's adopting a policy for car allowance and currency liquidity factors, the growth rate of auto insurance premiums in China increases substantially. In processing the model raw data, it is required to consider such aspects. (2) Model test[14] Gray prediction should go through the residual test, correlation test and posterior-variance-test. Residual Test (1) (1) (0) According to prediction model, we can work out ˆX,then regressive ˆX, get ˆX. Calculate (0) (0) residual as E [(1),(2), e e,()] e n X Xˆ (0) (0), and e( k) x ( k) xˆ ( k), k 1,2,, n Relative error: ek ( ) rel( k) 100%, k 1,2,, n (0) x ( k),if rel ( k ) <5%,testing passed. n Average relative error: 1 REL rel( k) n k 1 Correlation Test 0( ) 1( ) 0( ) 1( ) Calculate the Correlation coefficient: min X j X j max X j X j j j j X ( j) X ( j) X ( j) X ( j) 1 n j Calculate the correlation: n j 1 When =0.5, >0.6,testing passed. Posterior-variance-test max j Assuming the original sequence X (0),and residual series E, the variance is S 2 2 and S, n n 2 1 (0) 2 1 [ ( ) ], S2 [() ] n k e k e 1 n k 1 S x k x, the calculation posterior S C 2,Calculate the small S error probability pp{() e k e S1}, when P>0.95,C<0.35, model fits well. If all the above testing be passed, the model can be used and the accuracy is the first grade, otherwise residual need to be adjusted. (3) Model Analysis 1 1 2

5 As can be seen from Figure 3, this paper uses motor vehicles premium income sequences as the original data. The impact of data series length, index change method, background parameters and coincidence points on the prediction accuracy is analyzed. The other factors are constant when studying the correlation between single factor and the prediction accuracy.

6 Figure 3. Analysis results of predictive models in four aspects In traditional gray prediction model in the first group figure, only the sequence length is considered, the figure shows the average relative error and correlation degree. According to model checking, the appropriate sequence length is 4 or 5. In the last three groups, the sequence length is set as 13 in order to see the related impact more clearly. In the traditional gray prediction model, the average relative error is 14.78% when the sequence length is 13. From the last of the three groups in the above graph, it can be observed that the average relative error increases significantly. In this paper, when taking these four parameter values, both the average relative error and correlation degree should be satisfied. It does not work when obtaining a small average error while the correlation degree is less than 0.6. In this paper, we analyze the gray prediction model in terms of four effects that impacting prediction accuracy, and proposes improving way to traditional gray prediction model by analyzing the four aspects. Then the improved gray model is used to predict premiums for the next five years. 4. Forecast of motor vehicle premiums in next five years In this paper, when forecasting motor vehicle insurance premiums annually, we take the following four steps to determine the four factors that affect the premium income forecasting. The parameters got in each step would be used in the next step. So we can get a complete improved gray prediction model by accumulating. The first step is to determine the sequence length from the above analysis; the second step is smoothing the data sequence, and determining the index value; the third step is to determine the background parameters; the fourth step is to confirm the coincidence point when fitting. According to the above four steps above, we get motor vehicle insurance premium income forecasts in In July 2006, the "motor vehicle accident liability compulsory insurance policy" was published. It is a major reform in motor vehicle insurance industry. So, there is a difference between the original data on motor vehicle insurance before and after In this paper, in the first step of forecasting, we determine the input of model is data after Years Table 1. Predictive value of the premium from 2011 to 2015 Model Relation Poor ratio Correlation: estimates: error in of Percentage% R billion average % posterior Predictive value: billion In this paper, we do model checking to the premium forecast for As can be seen from Table I, the average premium relative error of the five-year forecast is small. Figure 1 shows that the premium growth rate have increased more in 2010 comparing with the previous years. It is inevitable

7 that premium data in will increased quickly. From a practical point of view, according to the studies of China's economic trends of Jin Sanlin on 2011, [15] In 2011, the international economic environment is relatively stable and the domestic economy will maintain continuity and stability and the economic growth throughout the year is expected to reach 9%. China's economic development trends are positively correlated with the motor vehicle insurance premium growth trends. From this point of view, premium forecast of is relatively high. However, according to Gu Xianghua for the future development trend of China's motor vehicle industry analysis. [16]During the twelfth Five-Year period, China's motor vehicle industry will maintain stable growth and the overall goal is to enhance the status of the motor vehicle industry in the world. Motor vehicles become more and more close to people's lives, popularity is increased, motor vehicle insurance industry is becoming more mature. The rapidly rising of motor vehicle insurance premium income becomes inevitable trend. Motor vehicle insurance premiums in is predicted by improved gray prediction model and is coincide with China's macroeconomic trends and motor vehicle industry trends in the next five years. 5. Conclusion This paper selects the gray model based on the analyses of the characteristics of existing insurance premiums predictive models and improves the traditional gray prediction model. The empirical results show high prediction accuracy. The forecast results show that in the twelfth five years, motor vehicle insurance premium income will remain fast and stable growth and the growth rate will remain about 25%. This paper also describes the significance of motor vehicle insurance premiums prediction and it mainly lies in the following areas: First, it helps to determine the premium rate of motor vehicle insurance correct and effectively. Determining the premium rate is helpful to effective operation and balance between benefits and risks. The prediction of premium income is the forecast of future market size, it is one of the factors affecting the premium rate determination. Second, it helps to set development goals and business plans of the insurance company. Based on the prediction, insurance companies can establish insurance funds and carry out insurance compensation and payments. Third, it helps to maintain social stability. With the increasing popularity of motor vehicles, motor vehicles and motor vehicle insurance play main role in the people spending. Motor vehicle insurance issues are also the focus of attention. Reasonable rate insures the interest of people and maintain the social stability. 6. Acknowledgments This work was supported by CIRC ministry class research plan Research on China vehicle insurance information sharing mechanism, HEGAOJI Important Plan (Grant No.: 2010zx ), China Postdoctoral Science Foundation funded project (Grant No.: ) and Beijing University of Technology Science Foundation (Grant No.: k4004) 7. References [1] Liu Yong-yang, Shen Sheng-mo, An qi-zhou, The Financial Structure and High-Tech Industries Development in China, JDCTA, Vol. 4, No. 9, pp. 80 ~ 87, 2010 [2] HU Hong-lei, The mathematical model of the premium and forecast,master thesis, 2003; HUANG Zuo-yan, WU Feng-ping, Development of China's insurance industry and forecasts the size of the premium, Prediction, [3] LIANG Xin, Prediction Shanghai Insurance premium income using neural network, Shanghai Engineering Technology University, [4] XIE Nai-ming, LIU Si-feng, Discrete GM (1,1) and mechanism of Gray Forecasting Model, Systems Engineering Theory and Practice, [5] Sun De-heng, Gao Ling, Li Ji-zhen, He Lin, Wang Ru-yi, The Performance Prediction and Early Warning of Network Based on Grey Model, AISS, Vol. 3, No. 10, pp. 497 ~ 504, 2011.

8 [6] XU Liang-liang, LIANG Gai-ge, WANG Jia-jia, The application of GM (1, 1) model in the premium income forecast, Modern Business Trade Industry, 2010, (11). [7] ZHAO Chang-li, CHEN Hai-yong, CHEN De-yang, Study of Gray Forecast Model to China's insurance premiums, Statistics and Decision, [8] DUAN Jia, JIN Ying, Study of gray method of Premium income forecast, Modern-commerce industry, 2008; [9] ZHANG Ji-lin, Prediction the scale of Chinese insurance premiums based on gray theory, Technology & Management Research, [10] LI Jun-feng, Gray system modeling theory and application, Zhejiang Sci-Tech University, [11] LI Cui-feng, Reaserch and application on gray system modeling theory, Zhejiang Gongshang University, [12] YAO Tian-xiang, LIU Si-feng, DANG Yao-guo. Discrete gray prediction model of optimize initial value, Systems Engineering and Electronics, [13] WEI Qin, CHEN Fei-yan, Elasticity demand analysis of China's motor vehicle insurance based on log-log model, Journel North China Electric Power University(Social Sciences), [14] LU Hui, Forecasts of Shanghai financial industry development trend based on gray prediction model, Economic Forum, [15] JIN San-lin, China's economic trends and macroeconomic policy orientation in 2011, Peking University School of Economics, China Opening Herald, 2010, (6). [16] GU Xiang-hua, China's motor vehicle industry operating status and future trends, China Rubber, 2010, 26(24).

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