Gaussian importance sampling and stratification: computational issues

This paper deals with efficient algorithms for simulating performance measures of Gaussian random vectors. Recently, we developed a simulation algorithm which consists of doing importance sampling by shifting the mean of the Gaussian random vector. Further variance reduction is obtained by stratification along a key direction. A central ingredient of this method is to compute the optimal shift of the mean for the importance sampling. The optimal shift is also a convenient, and in many cases, an effective direction for the stratification. After giving a brief overview of the basic simulation algorithms, we focus on issues regarding the computation of the optimal change of measure. A primary application of this methodology occurs in computational finance for pricing path dependent options