Stochastic models: simulation and heavy traffic analysis

UnrestrictedThis dissertation consists of two main parts: Monte Carlo Simulation and Heavy Traffic analysis. Much of the simulation part, chapter 1-3, is devoted to ways of improving simulation estimators in 3 different problems: Barrier Option Pricing, Random Knockout Tournaments, and System Reliability. Our efficiency criteria for comparing alternative estimators are variance and computing time. To achieve variance reduction, in addition to using combinations of different classical variance reduction techniques, innovative substantial sources of variance reduction are introduced by exploiting specific features of the problems under consideration. Second part of this dissertation, chapter 4-7, focuses on analyzing a stochastic control problem associated with a parallel server queueing system by employing Heavy Traffic approach. The stochastic control problem can not be solved exactly. We use heavy traffic limit theorems to derive an approximating control problem, referred to as Brownian control problem. Based on the Brownian control problem solution, we propose a control policy and then prove that our proposed policy isasymptotically optimal for the original control problem