Regression on Modeling Mean Excess Function of Extreme Losses
碩士 === 逢甲大學 === 統計與精算所 === 94 === Building a good model for the extreme losses has become an important issue due to many catastophes happened in recent years. The insurance loss distribution has a long right tail. Mcneil (1997) and Resnick (1997) suggested using Generalized Pareto Distribution (GPD)...
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| Format: | Others |
| Language: | zh-TW |
| Published: |
2006
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| Online Access: | http://ndltd.ncl.edu.tw/handle/79414593258418448029 |
| Summary: | 碩士 === 逢甲大學 === 統計與精算所 === 94 === Building a good model for the extreme losses has become an important issue due to many catastophes happened in recent years. The insurance loss distribution has a long right tail. Mcneil (1997) and Resnick (1997) suggested using Generalized Pareto Distribution (GPD) to model the data with extreme losses over the threhold. In this paper, we build the regression model of the mean excess fuction of the GPD based on textreme value theory. Under the null hypothesis which the threhold is a given value we can obtain the mean excess of every conditional value and then use them to build the regression model and test the null hypothesis. We estimate the threhold with the result of the test; estimate the shape parameter and the scale parameter with the intercept and the slope of the regression model. First, we simulated the Exp-GPD samples to verify our theory and some good results were shown. Then we used the Bootstrap method to obtain the averages and the standard deviations of the parameter estimates of the regression model and the GPD. Finally, after building the regression model we can apply it for the Conditional Tail Expectation (CTE) of the risk measures and the pure premium of extreme losses.
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