# Analysis of China Motor Vehicle Insurance Business Trends

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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.

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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