大離差理論在系統風險和投資組合最佳化的應用

Abstract

這份論文有兩部分。在第一部分，我們會用重要抽樣法來估計稀有事件的期望值。在常態分配或是布朗運動模型下，可以證明我們提出的方法是有效率的。我們也會說明如何應用重要抽樣法來評估系統風險。在第二部分，我們會應用大離差理論在有限時間的投資最佳化上面。

There are two parts in this paper. In the first part, we will focus on estimating the expectations under a rare event with the importance sampling method. Under Normal distribution or Brownian motion, we can prove that our proposed method is efficient. We will also show how to apply the importance sampling method to measure the systemic risk. In the second part, we will apply large deviation theory to the finite-horizon investment optimization.