蔡啟良2006-07-262018-07-092006-07-262018-07-092003http://ntur.lib.ntu.edu.tw//handle/246246/16272在此計畫中，將以傳統的連續時間風險模型（包含一個獨立的擴散過程）之保險 公司的盈餘過程為基礎，研究探討分別因振盪和保險理賠而導致破產時，破產時 間的現值之期望值（均為起始盈餘的函數）。當計算現值的貼現因子為零時，此 期望值變成分別因振盪和保險理賠而導致破產的機率。我想推導出上述期望值之 第n 次動差（如果存在的話）的遞迴公式和明確表式、漸近公式以及Tijms 近值 公式。此外，當保險理賠服從指數或伽瑪分配時，上述的期望值均有明確的公式 解。最後，我將尋找一些穩定而有效率的數值方法並計算這些期望值以及他們分 別所對應的動差。In this project, we would like to consider the insurer’s surplus process of the classical continuous time risk model containing an independent diffusion (Wiener) process. The expectations of the present values of the time of ruin due to oscillation and a claim, respectively, are studied. When the discount factor is set to zero, the expectations reduce to the probabilities of the time of ruin due to oscillation and a claim, respectively. The recursive formula and the explicit expression for the moments (if they exist) of, and the asymptotic formula and the Tijms approximation for, each of the expectations of the present values of the time of ruin are derived. In addition, explicit analytical solutions to these expectations can be obtained if the claim size distribution is an Exponential or a Gamma distribution. Finally, we will seek for some stable and effective numerical methods for computing the expectations of the present values of the time of ruin, and corresponding moments.application/pdf132064 bytesapplication/pdfzh-TW國立臺灣大學財務金融學系暨研究所擴散過程破產時間振盪遞迴公式漸近公式diffusion processtime of ruinoscillationrecursive formulaasymptotic formulareporthttp://ntur.lib.ntu.edu.tw/bitstream/246246/16272/1/912416H002020.pdf