汽車保險問題研究報告(一)

1、個人資料整理 僅限學習使用汽車保險問題的研究一）摘 要:利用某保險公司在開展汽車保險業(yè)務(wù)中所積累的具體數(shù)值資料,綜合分析影響續(xù)保率的因素、如承保車輛出現(xiàn)次數(shù)，承保車輛年齡，承保車輛品牌，承保車輛的使用性質(zhì)，承保車輛的銷售渠道，以及新車購買價格的不同等因素,應(yīng)用數(shù)理統(tǒng)計與數(shù)學實驗的方法,建立了一個汽車保險的簡單實用的數(shù)學模型,并根據(jù)相關(guān)數(shù)據(jù)的變動提供了改進模型的思路,該模型可為保險公司開展汽車保險業(yè)務(wù)提供較好的參考。關(guān)鍵詞: 汽車保險。續(xù)保率，影響因素，數(shù)學模型1.問題重述近幾年，國內(nèi)汽車銷售市場異常火爆，銷售量屢創(chuàng)新高。車輪上的世界，保險已經(jīng)與我們?nèi)缬半S形。汽車保險，簡稱車險，是指對機動車輛由

2、于自然災(zāi)害或意外事故所造成的人身傷亡或財產(chǎn)損失負賠償責任的一種商業(yè)保險。汽車保險是財產(chǎn)保險中的主要險種。自2006 年7 月1 日，交強險實施以來，車險與廣大車主間有了更加親密的關(guān)系。交強險，全稱機動車交通事故責任強制保險，是我國首個由國家法律規(guī)定實行的強制保險制度。交強險的基本定義是：交強險是由保險公司對被保險機動車發(fā)生道路交通事故造成受害人不包括本車人員和被保險人）的人身傷亡、財產(chǎn)損失，在責任限額內(nèi)予以賠償?shù)膹娭菩载熑伪ｋU。除了交強險，各個保險公司有自己的商業(yè)車險產(chǎn)品，種類繁多。在我國保險業(yè)，汽車保險有著不可撼動的地位。連續(xù)多年，汽車保險穩(wěn)居國內(nèi)產(chǎn)險業(yè)第一大險種?？梢哉f，對于財產(chǎn)保險公司來

3、說，得車險者得天下！2.問題分析評價一個保險公司的綜合影響力時，其市場份額具有舉足輕重的作用。近年來，由于越來越多的保險公司涉足車險市場，使得車險市場格局也發(fā)生了一些不容忽視的變化。當新的保險公司尋求自己的領(lǐng)地的時候，老的保險公司要做的除了發(fā)展新的領(lǐng)地，還要保住自己原有的客戶。很多保險公司開始關(guān)注續(xù)保率這個指標。續(xù)保率就是當年到期的客戶中續(xù)?？蛻羲嫉谋戎?。在續(xù)保數(shù)據(jù)中，我們發(fā)現(xiàn)承保車輛的使用性質(zhì)，承保車輛的銷售渠道以及新車購買價格的不同都會影響續(xù)保率。由具體數(shù)據(jù)可以看出：當年到期車輛續(xù)保率和目標客戶續(xù)保率的變化和幾種影響因素都有關(guān)。將不同時間的數(shù)據(jù)綜合列表，計算總體的平均值，并結(jié)合其對應(yīng)圖示

4、進行分析。3合理假設(shè)一：將不同時間的數(shù)據(jù)綜合列表，分別計算各個影響因素下當年到期車輛續(xù)保率和目標客戶續(xù)保率變化的總體平均值。個人資料整理 僅限學習使用一）按照承保車輛出現(xiàn)次數(shù)統(tǒng)計1）2018 年 9 月-2018 年 3 月當年到期車輛續(xù)保率及圖象201809201810201811201812201801201802201803出險 0 次20.01%20.71%20.53%20.97%36.44%37.05%35.68%出險 1 次29.38%29.93%29.96%30.51%41.73%42.82%42.12%出險 2 次33.74%34.46%34.85%35.56%46.94%48

5、.08%48.02%出險 3 次32.68%34.00%34.11%34.77%42.03%42.62%44.65%出險 4 次32.73%34.08%34.40%35.44%42.45%42.08%42.50%出險 5 次32.72%33.13%34.36%34.96%17.65%18.18%35.29%出險 5 次33.49%34.07%34.42%34.68%37.21%40.18%43.27%以上出險次數(shù)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 月目標客戶續(xù)保率及圖像201809201810201811201812201801201802201803出險 0 次20.17%20.89%20.87%21.26%36.53%37.13%35.80%出險 1 次33.39%34.31%34.86%35.58%43.53%44.55%44.92%出險 2 次出險 3 次出險 4 次出險 5 次出險 5 次以上出

7、險次數(shù)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%個人資料整理 僅限學習使用50.00%20100940.00%20101030.00%20.00%20101110.00%2010120.00）按照承保車輛年齡統(tǒng)計1）2018 年 9 月-2018 年 3 月當年到期車輛續(xù)保率及圖象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%上車齡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 月目標客戶續(xù)保率及圖像2018092018102018112018122018012018022018030-1 年21.95%22.35%21.95%22.48%35.30%35.52%35.62%平均值27.88%個人資料整理 僅限學習使用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%上車齡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）按照承保車輛品牌統(tǒng)計東南50.00%42.86%23.13%50.00%50.00%50.00%東風悅達53.79%51.72%44.32%58.48%55.34%53.79%起亞江鈴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%雪佛蘭吉利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、南馬自50.00%42.11%33.78%72.73%53.33%50.00%達長城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%吉林中國重汽35.71%32.77%20.16%20.00%13.95%35.71%東風標致36.92%33.33%31.07%25.93%33.33%36.92%南京依維34.62%33.33%29.93%60.00%50.00%34.62%柯東風本田48.88%46.64%34.86%46.97%45.79%48.88%廣州豐田45.40%43.64%31

15、.15%45.00%45.10%45.40%一汽馬自43.75%40.63%26.76%47.62%45.16%43.75%達一汽轎車41.91%43.81%26.05%46.43%45.35%41.91%(紅旗昌河鈴木23.60%21.69%21.25%21.95%19.67%23.60%華晨中華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%鄭州日產(chǎn)45.83%47.62%38.30%56.00%42.86%45.83%南

16、駿63.64%66.67%5.56%100.00%100.00%63.64%南京菲亞44.44%44.44%34.55%33.33%50.00%44.44%特躍進36.71%35.77%19.70%33.33%41.67%36.71%長豐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%紅塔北汽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%個人資料整理 僅限學習使用120.00%100.00%80.00%60.00%40.00%20.00%0.00%眾 安 代 杯 龍 瑞 放 木 亞利 城 致田 木通 特)值塔大 長 現(xiàn) 金 鐵

18、奇 解 鈴 起吉 長 標豐 鈴宇 亞均紅海京雪安 達風州 河菲平汽上北風長 悅東廣 昌京一東風南(放東解東南42.86%23.53%44.44%47.37%42.86%40.21%東風悅達51.72%44.61%56.02%53.79%51.72%51.57%起亞江鈴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%雪佛蘭吉利30.12%18.16%32.54%33.98%30.12%28.98%201011201011201012201101201102201103平均值個人資料整理 僅限學

19、習使用昌河26.83%19.19%23.26%28.57%26.83%24.94%海南馬自42.11%30.65%66.67%46.15%42.11%45.54%達長城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%吉林中國重汽32.77%19.71%22.73%16.22%32.77%24.84%東風標致33.33%30.00%15.15%27.12%33.33%27.79%南京依維33.33%28.80%50.00%45.45%33.33%38.18%柯東風本田46.64%34.90%

20、47.37%45.75%46.64%44.26%廣州豐田43.64%31.72%43.59%40.00%43.64%40.52%一汽馬自40.63%23.50%44.44%43.59%40.63%38.56%達一汽轎車43.81%23.33%48.84%45.45%43.81%41.05%(紅旗昌河鈴木21.69%19.49%21.05%19.30%21.69%20.64%華晨中華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、%鄭州日產(chǎn)47.62%37.35%65.00%46.67%47.62%48.85%南駿66.67%5.26%100.00%100.00%66.67%67.72%南京菲亞44.44%36.36%33.33%50.00%44.44%41.72%特躍進35.77%19.37%33.33%39.02%35.77%32.65%長豐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%紅塔北汽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%眾 安 代 杯 龍 瑞 放 木 亞利 城 致田 木 通特)值塔大 長 現(xiàn) 金 鐵 奇 解 鈴 起吉 長 標豐 鈴 宇亞均紅海京雪安 達風州 河菲平汽上北風長 悅東廣 昌京一東風南(放東解四）按照承保車輛使用性質(zhì)統(tǒng)計1）2018 年 9 月-2018 年 3 月當年到期車輛續(xù)保率及圖象201011201012201101201102201103平均值201809201810201811201812201801201802201803家庭自用25.81%26.53%

23、26.48%27.05%35.68%36.81%36.37%黨政機關(guān)客36.01%36.45%36.41%36.36%42.79%43.73%43.97%車平均值30.68%39.39%個人資料整理 僅限學習使用企業(yè)客車42.66%43.50%43.57%43.89%53.57%56.29%53.28%非營業(yè)貨車12.74%14.34%14.56%15.03%34.11%36.00%34.59%出租租賃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%公路客運25.98

24、%26.64%26.36%27.04%20.59%20.00%32.00%營業(yè)貨車17.59%17.81%17.32%17.42%30.26%33.64%34.55%特種車37.46%37.36%37.03%36.53%42.72%40.00%48.40%使用性質(zhì)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 月目標客戶續(xù)保率及圖像201809201810201811201812201801201802201803家庭自用23.57%24.40%24.46%24.85%34.25%35.28%34.71%黨政機關(guān)客33.99%34.12%34.07%34.39%39.19%40.21%40.97%車企業(yè)客車43.09%43.71%44.08%44.13%53.48%56.75%53.45%非營業(yè)貨車12.14%13.76%14.02%14.43%33.12%35.48%34.25%出租租賃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%公路客運27.89%29.65%29.41%30.56%18.75%18.18%28.89%營業(yè)貨車16.61%16.86%16.56%16.77%30.36%33.31%33.50%特種車36.49%36.31%35.98%35.53%43.01%39.35%47.99%使用性質(zhì)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%個人資料整理 僅限學習使用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）按照承保渠道統(tǒng)計1 ）2018 年 9 月-2018 年 3 月當年到期車輛續(xù)保率及圖象201809201810201811201812201801201802201803電話銷售39.41%40.00%40.00%40.00%交叉銷售19.94%19.02%19.14%19.83%16.67%26.47

28、%28.79%車商渠道32.25%40.38%41.95%44.30%53.70%53.05%50.00%合計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%電話銷售30.00%交叉銷售20.00%車商渠道10.00%合計0.00%201009 201010 201011 201012 201101 201102 2011032）2018 年 9 月-2018 年 3 月目標客戶續(xù)保率及圖像2018092018102018112018122018012

29、01802201803電話銷售48.40%25.00%25.00%25.00%交叉銷售16.94%16.54%16.73%17.67%13.33%23.33%27.12%車商渠道30.70%39.61%40.12%42.52%53.91%54.98%51.67%合計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%個人資料整理 僅限學習使用60.00%50.00%電話銷售40.00%交叉銷售30.00%20.00%車商渠道10.00%0.00%合計平均值六）按照新車購買價統(tǒng)計萬14.26%

30、14.59%14.85%15.45%31.55%33.80%31.26%5，10萬24.26%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%萬20，3029.52%30.84%30.67%30.64%40.59%40.04%41.44%萬30，5032.51%33.28%32.21%32.56%37.53%40.06%44.06%萬50，10029.53%30.21%29.31%30.23%38.10%37.99%38.75%萬100，33.92%33.94%31.02%30

31、.74%31.25%32.38%28.57%+萬新車購置23.22%23.88%23.78%24.27%38.26%38.99%37.88%價平均值平均值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平均值萬13.69%14.02%14.35%14.98%31.17%33.57%31.28%5，10萬22.79%23.18%

32、23.17%23.65%37.81%38.13%36.28%平均值21.87%29.29%個人資料整理 僅限學習使用10，2030.82%32.46%32.21%32.03%41.85%42.31%40.87%萬36.08%20，3028.09%29.57%29.43%29.05%40.49%38.70%40.44%萬33.68%30，5031.71%32.56%31.16%31.18%38.25%39.57%44.22%萬35.52%50，10028.57%29.10%28.64%29.50%41.13%39.33%40.30%萬33.80%100，35.71%34.59%31.10%30.

33、00%19.51%23.08%22.88%+萬28.13%新車購置21.28%22.00%22.03%22.46%37.21%37.84%36.66%價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( 二根據(jù)圖表可得出如下數(shù)據(jù)：當年到期車輛續(xù)保率目標客戶續(xù)保率承保車輛出現(xiàn)次數(shù)34.32%11.84%承保車輛年齡26.93%26.16%承保車輛品牌37.86%36.65%承保車輛的使用性質(zhì)38.3

34、5%37.55%承保車輛的銷售渠道34.10%39.76%新車購買價格的不同32.01%30.86%三）影響續(xù)保率的六種因素中相互之間有聯(lián)系，這些影響因素的重要性，影響力，或者優(yōu)先程度可以根據(jù)層析分析模型來定性和定量的描述。4. 模型的建立及求解一）層次分析法的基本步驟將續(xù)保率問題分解為三個層次，最上面的為目標層，即續(xù)保率；中間的為準則層，有承保車輛出現(xiàn)次數(shù)，承保車輛年齡，承保車輛品牌，承保車輛的使用性質(zhì)，承保車輛的銷售渠道，以及新車購買價格的不同；最下層為方案層，各層間的聯(lián)系用相連的直線表示。（2）通過相互比較確定的影響因素對于續(xù)保率的權(quán)重，及方案對于每一準則的權(quán)重，從而得到權(quán)重的定量方法。個人資料整理 僅限學習使用（3）將方案層對準則層的權(quán)重及準則層對目標層的權(quán)重進行綜合，最終確定方案層對目標層的權(quán)重。續(xù)保率當年到期車輛續(xù)保率目標客戶續(xù)保率照承承承承新承保保保保車保車車車車輛輛輛渠購輛年品使出齡牌用道買現(xiàn)性價次質(zhì)數(shù)二） 構(gòu)造成對比較矩陣設(shè)要比較的六個因素X x1, x2 , xn對續(xù)保率 Z 的影響，確定它們在 Z中所占的比重。比較第i 個元素與第j 個元素相對上一層某個因素的重要性時，使用數(shù)量化的相對權(quán)重 aij 來描述。共有6 個元素參與比較，則n=6 ）稱為成對比較矩陣。成對比較矩陣中 aij 的取值可參考Satty 的提議，按下述標度進行賦值。aij 在