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。

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.

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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