接管断裂失效概率估算的一种新方法

提出用分层抽样一拉丁抽样复合法计算接管的断裂失效概率，并与直接抽样的ＭｏｎｔｅＣａｒｌｏ法进行了比较。结果表明，用复合法计算接管断裂失效概率不但精度高，而且大幅度节省机时，提高效率。

Variance Reduction Technique for Estimating Value-at-Risk based on the Cross - Entropy

Value-at-Risk （VaR） estimation via Monte Carlo （MC） simulation is studied here. The variance reduction technique is proposed in order to speed up MC algorithm. The algorithm for estimating the probability of high portfolio losses （more general risk measure） based on the Cross - Entropy importance sampling is developed. This algorithm can easily be applied in any light- or heavy-tailed case without an extra adaptation. Besides, it does not loose in the performance in comparison to other known methods. A numerical study in both cases is performed and the variance reduction rate is compared with other known methods. The problem of VaR estimation using procedures for estimating the probability of high portfolio losses is also discussed.

Monte Carlo方法的最优源项偏倚抽样密度函数

Monte Carlo粒子输运中的源项偏倚抽样方法可以减小方差、提高计算效率。该文通过建立一个多区域分权重数学投篮模型,模拟了输运过程中的源项信息,得到了源项偏倚抽样方差最小时的最佳抽样密度函数解析式。采用随机数值方法对模型进行了计算,验证了函数的正确性,并举一例实际的粒子输运模拟问题,表明最优偏倚抽样方法对减小方差的效果显著。该方法可作为一种普适的减方差技巧应用于Monte Carlo粒子输运中,可用于构造粒子源参数(如位置、发射方向等)的最佳偏倚密度函数,尤其在分层抽样时能给出方差最小的最优各层比例系数。