標題: Portfolio Risk Management with Entropy Based Importance SamplingPortfolio Risk Management with Entropy Based Importance Sampling 作者: 李建武Li, Jian-Wu吳慶堂韓傳祥Wu,Ching-TangHan,Chuan-Hsiang應用數學系數學建模與科學計算碩士班 關鍵字: 風險管理;熵;蒙地卡羅;重點抽樣法;Risk Management;Entropy;Monte Carlo;Importance Sampling 公開日期: 2012 摘要: Abstract We provide an entropy-based importance sampling method to increase the accuracy for estimating default probabilities of some portfolios. The structure of these portfolios includes a summation of normal multivariate, a summation of student t multivariate, a mixture of normal variates and some student t variates , a summation of multi-dimensional geometric Brownian motions (basket of assets), and a summation of one dimensional geometric Brownian motion in different time (arithmetic sum in Asian option). The proposed entropy-based importance sampling method is a high-dimensional minimization problem of some relative entropy under some boundary constraint. It turns out this optimization problem is identical to some portfolio optimization problem under the classical mean-variance analysis. This relationship motivates a further study on computing the efficient frontiers of (1) portfolio consisting of multi-dimensional geometric Brownian motions and (2) portfolio as Asian weighted discrete time geometric Brownian motion.Abstract We provide an entropy-based importance sampling method to increase the accuracy for estimating default probabilities of some portfolios. The structure of these portfolios includes a summation of normal multivariate, a summation of student t multivariate, a mixture of normal variates and some student t variates , a summation of multi-dimensional geometric Brownian motions (basket of assets), and a summation of one dimensional geometric Brownian motion in different time (arithmetic sum in Asian option). The proposed entropy-based importance sampling method is a high-dimensional minimization problem of some relative entropy under some boundary constraint. It turns out this optimization problem is identical to some portfolio optimization problem under the classical mean-variance analysis. This relationship motivates a further study on computing the efficient frontiers of (1) portfolio consisting of multi-dimensional geometric Brownian motions and (2) portfolio as Asian weighted discrete time geometric Brownian motion. URI: http://140.113.39.130/cdrfb3/record/nctu/#GT079920503http://hdl.handle.net/11536/71810 顯示於類別： 畢業論文