The Mont e Carlo (II IC) Method is commonly used to approximat e mult ivariat e integrals, which can be interpreted as means of random variab... Show moreThe Mont e Carlo (II IC) Method is commonly used to approximat e mult ivariat e integrals, which can be interpreted as means of random variab les. The IIIC method uses th e sample mean to estimate the tr ue mean. In this thesis, we focus on minimizing th e sample size in MC simulat ion needed to sat isfy the specified error tolerance. Based on t he algorithm proposed by [5], we explain that t he cost of reliable IIIe est imat ion depends not only on variance but also on kurtosis. T herefore, when we try to improve th e efficiency of MC simulation by reducing variance, such as with Importance Sampling (IS), we need also look into the change of kurtosis. We analyze the change of cost in terms of the change of kur tosis and the change of variance. For a special case of IS we explore how to find th e optimal density in order to reduce variance. M.S. in Applied Mathematics, December 2013 Show less
