Stochastic Models (Management Science and Engineering)
IEORE4102 Stochastic Models (Management Science and Engineering)
The first two weeks will be a brief review of probability theory with emphasis on probability distributions that are of significant importance in the management and business end of operations research.
Poisson distribution, Normal distribution, lognormal distribution, gamma distribution, beta distribution, Student’s-T distribution; heavy-tailed versus light-tailed distributions.
The next several weeks will be a mix of learning how to simulate from the above distributions, as well as learning the basics of Markov chains in both discrete and continuous time (which includes an introduction to the Poisson process).
The binomial lattice model and random walks (including the gambler’s ruin problem) will be used as examples with applications in option pricing, risk and portfolio management and inventory.
Stopping times will be introduced as well.
The last several weeks will cover an introduction to Brownian motion, and geometric Brownian motion, how it can be simulated at a finite number of time points, and how it can be used to model risky assets, and other important processes in risk and portfolio management and inventory theory.