TITLE:  Topics in the Statistical Aspects of Simulation

ABSTRACT:

In the first part of the thesis, we apply various variance reduction techniques to the estimation of Asian averages and options and propose an easy-to-use quasi-Monte Carlo method that can provide significant variance reductions with minimal increases in computational time. We have also extended these techniques to estimate higher moments of the Asians averages.

In the second part, we then use these estimated moments to efficiently implement Gram-Charlier based estimators for probability distribution functions of Asian averages and options.

Finally, in the third part, we investigate a ranking and selection application that uses post hoc analysis to determine how the circumstances of procedure termination affect the probability of correct selection.