本文關鍵詞： 信用風險組合 罕見事件 尾概率 經(jīng)典兩步重要抽樣算法 零方差原則 最大值原則 重要分布函數(shù) 中心極限定理 Metroplis—Hastings算法　出處：《南京大學》2017年碩士論文　論文類型：學位論文

【摘要】：信用風險組合發(fā)生大額損失是一件罕見事件,但是一旦發(fā)生將造成嚴重后果。為了有效管理罕見事件發(fā)生造成的影響,首要任務是估計出罕見事件發(fā)生的概率,或尾概率。在計算中,由于罕見事件發(fā)生的概率很小,樣本量很少,從而導致估計方差過大。目前經(jīng)典的兩步重要抽樣算法在解決此問題時取得一定的成果,但是經(jīng)典方法在構造風險因子重要分布函數(shù)時采用零方差原則和最大值原則,得到的重要分布函數(shù)與理想狀況相差較大。本文根據(jù)零方差原則結合中心極限定理構造了新的重要分布函數(shù),并通過Metropolis-Hastings算法抽取風險因子的樣本,最終有效地減小了尾概率估計的方差。數(shù)據(jù)分析方面,通過與一般蒙特卡羅方法和經(jīng)典的兩步重要抽樣方法作數(shù)值比較,發(fā)現(xiàn)本文提出的算法能夠明顯減小尾概率估計的方差,得到預期效果。
[Abstract]:The occurrence of large portfolio credit risk loss is a rare event, but the event will cause serious consequences. In order to have the impact of effective management of the rare event, the first task is to estimate the probability of rare events, or tail probability. In the calculation, the probability of rare events is very small, small amount of sample, which leads to the estimation variance is too large. The classic two step important sampling algorithm made some achievements in solving this problem, but the classical method in constructing the important risk factor distribution function with zero variance principle and maximum principle, important distribution function and ideal conditions are different. According to the principle of combining the zero variance central limit theorem the distribution function of the new structure, and the risk factor of the sample Metropolis-Hastings algorithm, finally effectively reduces the variance of tail probability estimation. In the aspect of data analysis, by comparing with general Monte Carlo method and classic two step importance sampling method, it is found that the algorithm proposed in this paper can significantly reduce the variance of tail probability estimation and get the expected effect.

【學位授予單位】：南京大學
【學位級別】：碩士
【學位授予年份】：2017
【分類號】：O212.2
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本文編號：1497702