蔡啟良2006-07-262018-07-092006-07-262018-07-092005http://ntur.lib.ntu.edu.tw//handle/246246/16294在此計畫中，我將以傳統的連續時間風險模型之保險公司的盈餘過程為基礎，在等待時間 (即兩個相鄰保險理賠的間隔時間)服從獨立且相同之爾朗(2)分配的假設下，推導破產前一 瞬間的盈餘和破產時的不足額之貼現聯合和邊際分配和密度函數，以及導致破產的保險理 賠之貼現聯合和邊際分配和密度函數，並證明這些邊際分配和密度函數分別滿足一瑕更新 方程式。此外，我想嘗試探討這些分配和密度函數分別在不同爾朗(2)和爾朗(1)的假設下 是否有類似性。最後，我將尋找一些穩定而有效率的數值方法，在期初盈餘給定和保險理 賠服從指數分配的假設下，計算這些邊際分配和密度函數的值，做為保險公司和監理機關 的參考。In this project, we will try to derive explicit expressions for the discounted joint and marginal distribution and probability density functions of the surplus immediately prior to the time of ruin and the deficit at the time of ruin, and for the discounted distribution and probability density function of the amount of the claim causing ruin, based on Erlang(2) assumption. Also, we will want to show that these distribution and probability density functions satisfy defective renewal equations. Moreover, we hope we can find the similarity between expressions for these functions based on Erlang(1) and Erlang(2) processes, respectively. Finally, we would like to seek for some stable and effective numerical methods of computing the expressions for the discounted distribution and density functions, and get the numerical values for the insurer ’s and regulator ’s information if we the claim size is exponentially distributed.application/pdf190630 bytesapplication/pdfzh-TW國立臺灣大學財務金融學系暨研究所盈餘過程爾朗(2)過程破產時間貼現分配函數瑕更新方程式Surplus processErlang(2) processTime of ruinDiscounted distribution functionDefective renewal equation.reporthttp://ntur.lib.ntu.edu.tw/bitstream/246246/16294/1/932416H002048.pdf