在矩陣值隨機下對左尾端機率估計的漸進最佳重要抽樣法

Abstract

在風險管理的領域，多變數的分佈時常被用來測量一個系統內多個單位同時的違約機率。重要抽樣法時常被用來當作稀有事件的模擬。在常態分佈的假設下，我們證明了文中所給定的重要抽樣法對於矩陣值隨機的左尾端機率估計是漸進最佳的。在與其他的演算法比較下可以發現其優勢。此外，這樣的方法也可以拿來估計體系風險的問題。

In view of risk management, the tail probability of a multivariate distribution is a basic quantity to measure the occurrence of events that several components of a system collapse simultaneously. Importance sampling is commonly used for rare event simulation. Given the Gaussian distribution, we prove that our proposed importance sampling scheme is asymptotically optimal for matrix valued normal distributions and Brownian motions. Numerical comparisons with some commercial algorithm demonstrate superior of our proposed method. The importance sampling scheme can also be to study the systemic risk estimation.