嵌套模拟组合风险度量的方差减小  

Variance reduction techniques for nested simulation in measuring portfolio's risk

作　　者：孙永超[1] 吴倩[1] 徐承龙[1,2] 

机构地区：[1]同济大学数学系,上海200092 [2]上海市科学计算E-研究院及上海市科学计算重点实验室,上海200234

出　　处：《应用数学与计算数学学报》2016年第1期16-24,共9页Communication on Applied Mathematics and Computation

基　　金：国家自然科学基金资助项目(11171256);上海市教委计算科学E-研究院资助项目(E03004)

摘　　要：嵌套模拟是金融中非常复杂的问题,涉及的计算量很大.试图用方差减小技术来减小嵌套模拟估计的方差,进而减小均方误差,以减少计算成本,提高模拟效率.对要用嵌套模拟估计的风险度量,提出了对外层随机因子的双参数重要性抽样方法,以及对外层随机因子的单参数重要性抽样方法与控制变量方法结合的方法.数值实验表明,双参数重要性抽样法和单参数重要性抽样方法与控制变量方法结合的方法效果都比普通的单参数重要性抽样方法好.With large computational cost, nested simulation is a very complicated problem in finance. In this paper, we used variance reduction techniques to reduce variance of nested simulation, and to further reduce the mean square error and in- crease simulation efficiency. To estimate risk measure using nested simulation, we proposed a two parameters importance sampling method and a method which corn- bines one parameter importance method and control variate method. experiments demonstrate that these two methods aforementioned are than one parameter importance sampling methods.

关 键 词：嵌套模拟 重要性抽样 控制变量 回归 方差减小 

分 类 号：O212.1[理学—概率论与数理统计]