臺灣博碩士論文加值系統

近年來全球巨災頻傳，對巨災損失建構一適切之模型已成為全球再保險業之重要議題。保險損失分配為右偏之長尾分配，近年來已有許多文獻(Mcneil(1997)及Resnick (1997))均建議以廣義柏拉圖分配 (Generalized Pareto Distribution)(以下簡稱GPD分配)，來估計損失模型之極值損失部分，其結果較傳統模型為佳。本文以此理論為基礎，發展出GPD分配平均餘額函數之迴歸模型，在虛無假設為門檻值等於某一數值的前提下，計算各條件值的平均餘額，然後再以此餘額樣本建立平均餘額函數之迴歸模型，並作假設檢定。以檢定結果及迴歸模型的截距及斜率估計GPD分配之門檻值、形狀參數、規模參數。本文先模擬一Exp-GPD分配的樣本以驗證參數估計的效果，研究結果顯示有不錯的準確性。再以拔靴法(Bootstrap)重複抽樣法估計GPD分配平均餘額函數之迴歸模型參數估計值的平均數及標準差並計算其信賴區間。最後，迴歸模型建立後可應用於計算風險量度中的尾部條件期望值 (Conditional Tail Expectation,CTE)及計算極值損失的純保費。

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.

第一章 緒論…………………………………………………………1
第一節 研究動機與目的………………………………………1
第二節 文獻回顧………………………………………………3
第三節 研究架構與內容………………………………………5
第二章 模型假設與研究方法………………………………………6
第一節 GPD分配與平均餘額函數……………………………6
第二節 平均餘額函數之迴歸…………………………………9
第三節 參數估計與模型門檻值假設檢定……………………11
第三章 實例的探討…………………………………………………14
第一節 Exp-GPD分配模擬分析………………………………14
第二節 實例建模與分析………………………………………22
第三節 平均餘額函數迴歸模型之應用………………………28
第四章 結論…………………………………………………………30
第一節 結論……………………………………………………30
參考文獻…………………………………………………………………32
附錄一 條件餘額的期望值與變異數…………………………………34
附錄二 GPD平均餘額函數之迴歸參數公式推導……………………38
附錄三 程式……………………………………………………………40

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