汽车保险问题研究报告(一)

1、个人资料整理 仅限学习使用汽车保险问题的研究一）摘 要:利用某保险公司在开展汽车保险业务中所积累的具体数值资料,综合分析影响续保率的因素、如承保车辆出现次数，承保车辆年龄，承保车辆品牌，承保车辆的使用性质，承保车辆的销售渠道，以及新车购买价格的不同等因素,应用数理统计与数学实验的方法,建立了一个汽车保险的简单实用的数学模型,并根据相关数据的变动提供了改进模型的思路,该模型可为保险公司开展汽车保险业务提供较好的参考。关键词: 汽车保险。续保率，影响因素，数学模型1.问题重述近几年，国内汽车销售市场异常火爆，销售量屡创新高。车轮上的世界，保险已经与我们如影随形。汽车保险，简称车险，是指对机动车辆由

2、于自然灾害或意外事故所造成的人身伤亡或财产损失负赔偿责任的一种商业保险。汽车保险是财产保险中的主要险种。自2006 年7 月1 日，交强险实施以来，车险与广大车主间有了更加亲密的关系。交强险，全称机动车交通事故责任强制保险，是我国首个由国家法律规定实行的强制保险制度。交强险的基本定义是：交强险是由保险公司对被保险机动车发生道路交通事故造成受害人不包括本车人员和被保险人）的人身伤亡、财产损失，在责任限额内予以赔偿的强制性责任保险。除了交强险，各个保险公司有自己的商业车险产品，种类繁多。在我国保险业，汽车保险有着不可撼动的地位。连续多年，汽车保险稳居国内产险业第一大险种。可以说，对于财产保险公司来

3、说，得车险者得天下！2.问题分析评价一个保险公司的综合影响力时，其市场份额具有举足轻重的作用。近年来，由于越来越多的保险公司涉足车险市场，使得车险市场格局也发生了一些不容忽视的变化。当新的保险公司寻求自己的领地的时候，老的保险公司要做的除了发展新的领地，还要保住自己原有的客户。很多保险公司开始关注续保率这个指标。续保率就是当年到期的客户中续保客户所占的比重。在续保数据中，我们发现承保车辆的使用性质，承保车辆的销售渠道以及新车购买价格的不同都会影响续保率。由具体数据可以看出：当年到期车辆续保率和目标客户续保率的变化和几种影响因素都有关。将不同时间的数据综合列表，计算总体的平均值，并结合其对应图示

4、进行分析。3合理假设一：将不同时间的数据综合列表，分别计算各个影响因素下当年到期车辆续保率和目标客户续保率变化的总体平均值。个人资料整理 仅限学习使用一）按照承保车辆出现次数统计1）2018 年 9 月-2018 年 3 月当年到期车辆续保率及图象201809201810201811201812201801201802201803出险 0 次20.01%20.71%20.53%20.97%36.44%37.05%35.68%出险 1 次29.38%29.93%29.96%30.51%41.73%42.82%42.12%出险 2 次33.74%34.46%34.85%35.56%46.94%48

5、.08%48.02%出险 3 次32.68%34.00%34.11%34.77%42.03%42.62%44.65%出险 4 次32.73%34.08%34.40%35.44%42.45%42.08%42.50%出险 5 次32.72%33.13%34.36%34.96%17.65%18.18%35.29%出险 5 次33.49%34.07%34.42%34.68%37.21%40.18%43.27%以上出险次数23.22%23.88%23.78%24.27%38.26%38.99%37.88%平均值平均值27.34%35.21%40.24%37.84%37.67%29.47%36.76%30

6、.04%34.32%60.00%20100950.00%20101040.00%20101130.00%20.00%20101210.00%2011010.00%201102201103平均值2）2018 年 9 月-2018 年 3 月目标客户续保率及图像201809201810201811201812201801201802201803出险 0 次20.17%20.89%20.87%21.26%36.53%37.13%35.80%出险 1 次33.39%34.31%34.86%35.58%43.53%44.55%44.92%出险 2 次出险 3 次出险 4 次出险 5 次出险 5 次以上出

7、险次数21.28%22.00%22.03%22.46%37.21%37.84%36.66%平均值平均值27.52%38.73%0.00%0.00%0.00%0.00%0.00%28.50%31.58%个人资料整理 仅限学习使用50.00%20100940.00%20101030.00%20.00%20101110.00%2010120.00）按照承保车辆年龄统计1）2018 年 9 月-2018 年 3 月当年到期车辆续保率及图象2018092018102018112018122018012018022018030-1 年24.83%25.22%25.0

8、6%25.84%37.27%37.76%37.81%1-2 年27.45%29.08%28.81%29.22%44.77%46.28%45.35%2-3 年21.64%22.24%22.19%22.37%37.09%39.03%37.22%3-4 年21.16%21.95%21.86%21.71%35.31%36.85%35.34%4-5 年18.50%18.42%18.34%18.70%33.68%32.78%29.00%5-6 年17.23%17.82%18.00%18.34%38.24%38.21%37.24%6-7 年18.01%18.45%18.74%18.96%43.78%39.2

9、2%36.39%7-8 年19.66%20.07%20.06%20.14%36.84%32.49%34.41%8-9 年18.92%19.80%20.24%20.21%28.00%26.42%26.85%9-10 年16.47%17.12%16.82%17.71%35.71%33.87%25.36%10 年以16.51%16.49%16.41%16.76%18.52%25.48%25.65%上车龄23.22%23.88%23.78%24.27%38.26%38.99%37.88%平均值平均值30.54%35.85%28.83%27.74%24.20%26.44%27.65%26.24%22.9

10、2%23.29%19.40%30.04%26.93%50.00%45.00%20100940.00%35.00%20101030.00%20101125.00%20.00%20101215.00%20110110.00%2011025.00%0.00%201103平均值2）2018 年 9 月-2018 年 3 月目标客户续保率及图像2018092018102018112018122018012018022018030-1 年21.95%22.35%21.95%22.48%35.30%35.52%35.62%平均值27.88%个人资料整理 仅限学习使用1-2 年25.79%27.71%28.0

11、3%28.74%45.00%45.89%44.48%2-3 年20.69%21.28%21.56%21.90%35.79%38.36%37.00%3-4 年20.37%21.23%21.50%21.25%35.19%36.53%34.54%4-5 年17.56%17.47%17.45%17.92%33.65%32.76%29.40%5-6 年16.62%17.16%17.42%17.85%36.26%36.90%35.89%6-7 年17.10%17.48%18.01%18.11%43.69%40.06%36.35%7-8 年18.86%19.07%19.20%19.27%36.07%30.9

12、4%32.70%8-9 年18.77%19.52%19.79%19.86%28.17%27.84%26.83%9-10 年16.01%16.52%16.39%17.44%35.71%34.43%26.32%10 年以16.44%16.48%16.62%17.03%18.00%24.83%25.35%上车龄21.28%22.00%22.03%22.46%37.21%37.84%36.66%平均值35.09%28.08%27.23%23.74%25.45%27.26%25.16%22.97%23.26%19.25%28.50%26.16%50.00%20100940.00%20101030.00%

13、20101120.00%20101210.00%2011010.00%201102201103平均值三）按照承保车辆品牌统计东南50.00%42.86%23.13%50.00%50.00%50.00%东风悦达53.79%51.72%44.32%58.48%55.34%53.79%起亚江铃37.30%36.52%27.01%25.00%27.78%37.30%上海通用41.19%38.31%32.49%36.57%38.63%41.19%雪佛兰吉利31.35%30.12%18.63%32.41%34.32%31.35%昌河27.48%26.83%19.51%25.53%29.41%27.48%海

14、南马自50.00%42.11%33.78%72.73%53.33%50.00%达长城34.94%33.33%28.57%35.71%32.43%34.94%解放(一汽35.45%35.24%16.51%20.75%32.65%35.45%吉林中国重汽35.71%32.77%20.16%20.00%13.95%35.71%东风标致36.92%33.33%31.07%25.93%33.33%36.92%南京依维34.62%33.33%29.93%60.00%50.00%34.62%柯东风本田48.88%46.64%34.86%46.97%45.79%48.88%广州丰田45.40%43.64%31

15、.15%45.00%45.10%45.40%一汽马自43.75%40.63%26.76%47.62%45.16%43.75%达一汽轿车41.91%43.81%26.05%46.43%45.35%41.91%(红旗昌河铃木23.60%21.69%21.25%21.95%19.67%23.60%华晨中华39.29%35.71%26.07%36.84%36.36%39.29%北京(福0.00%2.17%1.52%0.00%0.00%0.00%田宇通45.45%33.33%42.86%28.57%25.00%45.45%郑州日产45.83%47.62%38.30%56.00%42.86%45.83%南

16、骏63.64%66.67%5.56%100.00%100.00%63.64%南京菲亚44.44%44.44%34.55%33.33%50.00%44.44%特跃进36.71%35.77%19.70%33.33%41.67%36.71%长丰36.05%34.67%28.35%28.00%25.00%36.05%解放(一汽37.50%36.67%23.00%0.00%27.27%37.50%红塔北汽43.27%40.22%20.99%47.06%64.29%43.27%品牌37.88%36.66%24.27%38.26%38.99%37.88%平均值30.44%30.48%44.34%28.91%

17、38.38%38.98%41.52%34.58%56.59%44.33%52.91%31.82%38.06%29.70%26.04%50.32%33.32%29.34%26.39%32.92%40.42%45.34%42.61%41.28%40.91%21.96%35.59%0.62%36.78%46.07%66.58%41.87%33.98%31.35%26.99%43.18%35.66%37.86%个人资料整理 仅限学习使用120.00%100.00%80.00%60.00%40.00%20.00%0.00%众 安 代 杯 龙 瑞 放 木 亚利 城 致田 木通 特)值塔大 长 现 金 铁

18、奇 解 铃 起吉 长 标丰 铃宇 亚均红海京雪安 达风州 河菲平汽上北风长 悦东广 昌京一东风南(放东解东南42.86%23.53%44.44%47.37%42.86%40.21%东风悦达51.72%44.61%56.02%53.79%51.72%51.57%起亚江铃36.52%25.42%28.00%29.41%36.52%31.17%上海通用38.31%32.39%35.87%37.04%38.31%36.38%雪佛兰吉利30.12%18.16%32.54%33.98%30.12%28.98%201011201011201012201101201102201103平均值个人资料整理 仅限学

19、习使用昌河26.83%19.19%23.26%28.57%26.83%24.94%海南马自42.11%30.65%66.67%46.15%42.11%45.54%达长城33.33%26.92%33.52%29.97%33.33%31.41%解放(一汽35.24%16.14%20.00%32.98%35.24%27.92%吉林中国重汽32.77%19.71%22.73%16.22%32.77%24.84%东风标致33.33%30.00%15.15%27.12%33.33%27.79%南京依维33.33%28.80%50.00%45.45%33.33%38.18%柯东风本田46.64%34.90%

20、47.37%45.75%46.64%44.26%广州丰田43.64%31.72%43.59%40.00%43.64%40.52%一汽马自40.63%23.50%44.44%43.59%40.63%38.56%达一汽轿车43.81%23.33%48.84%45.45%43.81%41.05%(红旗昌河铃木21.69%19.49%21.05%19.30%21.69%20.64%华晨中华35.71%25.48%34.78%32.39%35.71%32.82%北京(福2.17%1.54%27.27%15.79%2.17%9.79%田宇通33.33%40.74%0.00%0.00%33.33%21.48

21、%郑州日产47.62%37.35%65.00%46.67%47.62%48.85%南骏66.67%5.26%100.00%100.00%66.67%67.72%南京菲亚44.44%36.36%33.33%50.00%44.44%41.72%特跃进35.77%19.37%33.33%39.02%35.77%32.65%长丰34.67%25.31%26.09%25.00%34.67%29.15%解放(一汽36.67%23.39%0.00%27.27%36.67%24.80%红塔北汽40.22%19.92%43.75%63.89%40.22%41.60%品牌36.66%22.46%37.21%37.

22、84%36.66%34.16%平均值36.65%120.00%100.00%80.00%60.00%40.00%20.00%0.00%众 安 代 杯 龙 瑞 放 木 亚利 城 致田 木 通特)值塔大 长 现 金 铁 奇 解 铃 起吉 长 标丰 铃 宇亚均红海京雪安 达风州 河菲平汽上北风长 悦东广 昌京一东风南(放东解四）按照承保车辆使用性质统计1）2018 年 9 月-2018 年 3 月当年到期车辆续保率及图象201011201012201101201102201103平均值201809201810201811201812201801201802201803家庭自用25.81%26.53%

23、26.48%27.05%35.68%36.81%36.37%党政机关客36.01%36.45%36.41%36.36%42.79%43.73%43.97%车平均值30.68%39.39%个人资料整理 仅限学习使用企业客车42.66%43.50%43.57%43.89%53.57%56.29%53.28%非营业货车12.74%14.34%14.56%15.03%34.11%36.00%34.59%出租租赁31.72%32.29%32.56%33.28%75.08%70.26%50.97%城市公交70.83%70.72%70.67%70.80%90.91%86.36%72.22%公路客运25.98

24、%26.64%26.36%27.04%20.59%20.00%32.00%营业货车17.59%17.81%17.32%17.42%30.26%33.64%34.55%特种车37.46%37.36%37.03%36.53%42.72%40.00%48.40%使用性质23.22%23.88%23.78%24.27%38.26%38.99%37.88%平均值48.11%23.05%46.59%76.07%25.52%24.08%39.93%30.04%38.35%100.00%20100980.00%20101060.00%20101140.00%20101220.00%2011010.00%201

25、102201103平均值2）2018 年 9 月-2018 年 3 月目标客户续保率及图像201809201810201811201812201801201802201803家庭自用23.57%24.40%24.46%24.85%34.25%35.28%34.71%党政机关客33.99%34.12%34.07%34.39%39.19%40.21%40.97%车企业客车43.09%43.71%44.08%44.13%53.48%56.75%53.45%非营业货车12.14%13.76%14.02%14.43%33.12%35.48%34.25%出租租赁32.28%32.86%33.28%34.2

26、0%74.42%70.00%52.63%城市公交68.75%68.51%68.11%68.11%91.84%86.67%71.08%公路客运27.89%29.65%29.41%30.56%18.75%18.18%28.89%营业货车16.61%16.86%16.56%16.77%30.36%33.31%33.50%特种车36.49%36.31%35.98%35.53%43.01%39.35%47.99%使用性质21.28%22.00%22.03%22.46%37.21%37.84%36.66%平均值平均值28.79%36.71%48.38%22.46%47.10%74.72%26.19%23.

27、42%39.24%28.50%37.55%个人资料整理 仅限学习使用100.00%90.00%80.00%20100970.00%20101060.00%50.00%20101140.00%20101230.00%20.00%20110110.00%2011020.00%201103平均值五）按照承保渠道统计1 ）2018 年 9 月-2018 年 3 月当年到期车辆续保率及图象201809201810201811201812201801201802201803电话销售39.41%40.00%40.00%40.00%交叉销售19.94%19.02%19.14%19.83%16.67%26.47

28、%28.79%车商渠道32.25%40.38%41.95%44.30%53.70%53.05%50.00%合计23.22%23.88%23.78%24.27%38.26%38.99%37.88%平均值平均值39.85%21.41%45.09%30.04%34.10%60.00%50.00%40.00%电话销售30.00%交叉销售20.00%车商渠道10.00%合计0.00%201009 201010 201011 201012 201101 201102 2011032）2018 年 9 月-2018 年 3 月目标客户续保率及图像2018092018102018112018122018012

29、01802201803电话销售48.40%25.00%25.00%25.00%交叉销售16.94%16.54%16.73%17.67%13.33%23.33%27.12%车商渠道30.70%39.61%40.12%42.52%53.91%54.98%51.67%合计21.28%22.00%22.03%22.46%37.21%37.84%36.66%平均值平均值30.85%17.42%43.64%27.14%29.76%个人资料整理 仅限学习使用60.00%50.00%电话销售40.00%交叉销售30.00%20.00%车商渠道10.00%0.00%合计平均值六）按照新车购买价统计万14.26%

30、14.59%14.85%15.45%31.55%33.80%31.26%5，10万24.26%24.62%24.56%25.10%39.30%39.61%37.70%10，2031.97%33.27%32.81%32.89%42.67%43.08%42.49%万20，3029.52%30.84%30.67%30.64%40.59%40.04%41.44%万30，5032.51%33.28%32.21%32.56%37.53%40.06%44.06%万50，10029.53%30.21%29.31%30.23%38.10%37.99%38.75%万100，33.92%33.94%31.02%30

31、.74%31.25%32.38%28.57%+万新车购置23.22%23.88%23.78%24.27%38.26%38.99%37.88%价平均值平均值22.25%30.74%37.03%34.82%36.03%33.45%31.69%30.04%32.01%50.00%45.00%40.00%20100935.00%20101030.00%25.00%20101120.00%20101215.00%20110110.00%5.00%2011020.00%201103平均值万13.69%14.02%14.35%14.98%31.17%33.57%31.28%5，10万22.79%23.18%

32、23.17%23.65%37.81%38.13%36.28%平均值21.87%29.29%个人资料整理 仅限学习使用10，2030.82%32.46%32.21%32.03%41.85%42.31%40.87%万36.08%20，3028.09%29.57%29.43%29.05%40.49%38.70%40.44%万33.68%30，5031.71%32.56%31.16%31.18%38.25%39.57%44.22%万35.52%50，10028.57%29.10%28.64%29.50%41.13%39.33%40.30%万33.80%100，35.71%34.59%31.10%30.

33、00%19.51%23.08%22.88%+万28.13%新车购置21.28%22.00%22.03%22.46%37.21%37.84%36.66%价28.50%平均值30.86%50.00%45.00%20100940.00%35.00%20101030.00%20101125.00%20.00%20101215.00%10.00%2011015.00%2011020.00%201103平均值( 二根据图表可得出如下数据：当年到期车辆续保率目标客户续保率承保车辆出现次数34.32%11.84%承保车辆年龄26.93%26.16%承保车辆品牌37.86%36.65%承保车辆的使用性质38.3

34、5%37.55%承保车辆的销售渠道34.10%39.76%新车购买价格的不同32.01%30.86%三）影响续保率的六种因素中相互之间有联系，这些影响因素的重要性，影响力，或者优先程度可以根据层析分析模型来定性和定量的描述。4. 模型的建立及求解一）层次分析法的基本步骤将续保率问题分解为三个层次，最上面的为目标层，即续保率；中间的为准则层，有承保车辆出现次数，承保车辆年龄，承保车辆品牌，承保车辆的使用性质，承保车辆的销售渠道，以及新车购买价格的不同；最下层为方案层，各层间的联系用相连的直线表示。（2）通过相互比较确定的影响因素对于续保率的权重，及方案对于每一准则的权重，从而得到权重的定量方法。个人资料整理 仅限学习使用（3）将方案层对准则层的权重及准则层对目标层的权重进行综合，最终确定方案层对目标层的权重。续保率当年到期车辆续保率目标客户续保率照承承承承新承保保保保车保车车车车辆辆辆渠购辆年品使出龄牌用道买现性价次质数二） 构造成对比较矩阵设要比较的六个因素X x1, x2 , xn对续保率 Z 的影响，确定它们在 Z中所占的比重。比较第i 个元素与第j 个元素相对上一层某个因素的重要性时，使用数量化的相对权重 aij 来描述。共有6 个元素参与比较，则n=6 ）称为成对比较矩阵。成对比较矩阵中 aij 的取值可参考Satty 的提议，按下述标度进行赋值。aij 在