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系統識別號 U0002-0306201114365200
中文論文名稱 汽車車體損失險的預期損失與相依結構探討
英文論文名稱 The Expected Loss and Dependence Structure Analysis of Automobile Physical Damage Insurance
校院名稱 淡江大學
系所名稱(中) 財務金融學系碩士班
系所名稱(英) Department of Banking and Finance
學年度 99
學期 2
出版年 100
研究生中文姓名 陳威宇
研究生英文姓名 Wei-Yu Chen
學號 698530473
學位類別 碩士
語文別 英文
口試日期 2011-05-12
論文頁數 54頁
口試委員 指導教授-李沃牆
委員-洪明欽
委員-顧廣平
委員-何宗武
中文關鍵字 汽車車體損失險  預期損失  極端值  copula模型  關連結構 
英文關鍵字 automobile physical damage insurance  Expect shortfall  Extreme value  copula function  Hill plot 
學科別分類 學科別社會科學商學
中文摘要 次貸風暴所引發的連鎖效應對全球金融市場造成巨大的衝擊,也讓全球重新省思風險管理的價值。其中又以美國國際集團(AIG)的破產事件影響最鉅,因此本文以台灣某產險公司的汽車車體損失險為研究對象,評估該險種損失分配與相依結構。首先利用損失因子對損失資料做交叉分析與分量迴歸分析;再利用一般化柏拉圖極端值模型(GPD)分別計算95%、97.5%與99%信賴水準下的風險值,透過拔靴複製法來估計其信賴區間並檢測模型績效;最後使用四種copula模型來檢測甲、乙與丙式汽車車體損失險之間的關聯性。實證結果顯示,GPD模型能夠精準的配適損失資料的尾端部分,在99%的信賴水準為下,預期損失為469409.6738,損失超過50萬的機率為0.25%。甲、乙與丙式險種之間的相依結構極低,隱含三式車險之間彼此獨立。
英文摘要 After the 2007 finance crisis, the risk management is more noticeable in recent years, but there is still very limited number of general literatures on automobile physical insurance. This paper focuses on modeling and estimating tail parameters of automobile physical damage loss severity. At an attempt to do so, firstly, the cross analysis and quantile regression are used to examine the correlations between risk factors and loss. Then, we proceed with a simple exploratory loss data analysis using Q-Q plot and cross analysis. Furthermore, we determine the thresholds of GPD through mean excess plot and Hill plot. Value at Risk and the expected shortfall are also calculated. Bootstrap method is taken into account to estimate the confidence interval of parameters. Empirical results show that the GPD method is a theoretically well supported technique for fitting a parametric distribution to the tail of an unknown underlying distribution. Copula functions are also applied to fit the rank correlation between different loss types. From the results, it is concluded that the GPD model can capture the behavior of the loss severity tail of automobile physical damage insurance very well.
論文目次 Contents
Contents V
Figure Contents VII
Table Contents VIII
Chapter 1: Introduction 1
1.1 Motivation 1
1.2 Research objectives 3
1.3 The flow chart 4
Chapter 2: Literature Review 5
2.1 Loss data and extreme value distribution 5
2.2 Copula function 7
Chapter3: Methodologies 8
3.1 Extreme value distribution 8
3.1.1 The GEV distribution 10
3.1.2 Generalized Pareto distribution 11
3.1.3 Steps in applying GPD 12
3.1.4 Threshold selection 13
3.1.5 Expected shortfall 16
3.2 Copula function 17
Chapter4: Results and Analysis 20
4.1 Data description 20
4.2 Cross analysis 20
4.3 Quantile regression analysis 28
4.4 Extreme value analysis 33
4.5 Copula analysis 42
4.5.1 Copula analysis between loss type A and loss type B 42
4.5.2 Copula analysis between loss type A and loss type C 44
4.5.3 Copula analysis between loss type B and loss type C 45
Chapter 5 Conclusions 47
References 49
Figure Contents
Figure 1: The flow chart 4
Figure 2: The 95% confidence interval between the risk factors and loss 32
Figure 3(a): 1-F(x)on logarithmic scaling in x-axis 35
Figure 3(b): 1-F(x) for empirical distribution of a sample. 35
Figure 3(c): P-P plot for loss data 35
Figure 3(d): Q-Q plot for loss data 35
Figure 4(a): The Lognormal pdf plot of loss amount 37
Figure 4(b): The Exponential pdf plot of loss amount 37
Figure 5: The mean excess function of loss amount 38
Figure 6: The Hill plot of loss amount 39
Figure 7: The Bootstrap estimate of parameter (Threshold =11900) 41
Figure 8: The cdf of empirical copula 43
Figure 9: The 3d histogram for u & v 43
Figure 10: The cdf of empirical copula 44
Figure 11: The 3d histogram for u & v 44
Figure 12: The cdf of empirical copula 46
Figure 13: The 3d histogram for u & v 46
Table Contents
Table 1: All the input factors 22
Table 2: Summary of cross-analysis 23
Table 3: Cross-analysis between loss and type of automobile physical damage loss 23
Table 4: Cross-analysis between loss and sex 24
Table 5: Cross-analysis between loss and age 24
Table 6: Cross-analysis between loss and age of vehicle 25
Table 7: Cross-analysis between loss and engine displacement 26
Table 8: Cross-analysis between loss and marriage 27
Table 9: The correlations between all the input factors and loss data 27
Table 10: The results of Quantile Regression between sex and loss 29
Table 11: The results of Quantile Regression between age and loss 29
Table 12: The results of Quantile Regression between age of vehicle and loss 30
Table 14: The results of Quantile Regression between marriage and loss 31
Table 15: Frequencies of loss data 34
Table 16: Summary statistics for Loss data 35
Table 17: Parametric estimations for fitted functions 36
Table 18: The VaR and ES of GPD 39
Table 19: Bootstrapa confidence intervals for the GPD 40
Table 20: The Estimate Results of Copula Functions-Loss type A & Loss type B 43
Table 21: The Estimate Results of Copula Functions-Loss type A & Loss type C 45
Table 22: The Estimate Results of Copula Functions-Loss type B & Loss type C 46




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