Course catalog description: Review of basics of simulation; random number generation. Output analysis; variance reduction. Some Stochastic processes - Wiener Process, Markov Processes; and Stochastic Calculus. Introduction to continuous systems, modeling continuous deterministic systems, Numerical simulation of deterministic systems. Introduction to continuous systems with random components, Modeling using Stochastic differential equations. Application systems: Finance - Option pricing, Risk management, Neuro-computing, Biological systems, Hydrological sciences, Meteorology, Geology and Operations Research. Simulation of continuous, stochastic systems modeled using stochastic differential equations. Options Pricing for vanilla options and exotic options; Feynman-Kac Formula. Equivalent Martingale Measure pricing; Girsanov's Theorem. Hedging strategies; Option Pricing under incomplete market. Stochastic Volatility; Jump Diffusion Models.
If time permits: Controlling a Stochastic system. Stochastic Control; Intro to Stochastic Dynamic Programming. Simulation based Optimization Extensive computer-based simulation. Prerequisite: DSES-6620 or permission of instructor. 3 credit hours
Last modified: Thu Oct 19 12:43:11 EDT 2006