ADAPTIVE STOCHASTIC SIMULATION FOR STRUCTURED PROBLEMS

In this thesis, I examine several situations in which one can improve the efficiency of a stochastic simulation algorithm by adaptively exploiting special structure of the problem at hand. The thesis is comprised of three independent papers. In the first paper, I propose a new variance reduction technique in the setting of comparing the per-formance of two stochastic systems. The technique is a natural generalization of common random number sampling, a well-known sampling strategy that may reduce variance in certain situations. Common random number sampling entails sampling the underlying uniform random variates according to a particular copula; my proposed method considers more general copulae. I identify properties such a copula must have in order to induce a valid sampling strategy, give examples of situations in which copulae exist that outperform common random numbers, and give an algorithm for computing an effective Gaussian copula. In the second paper, I discuss an automated procedure for computing a control variate for the pricing of American options. The control variate is equal to th