SYLLABUS/PREREQUISITES for : IEOR 4106. Stochastic Models
FAll 2018, Professor K. Sigman
Some of the main stochastic models used
in engineering and operations research applications: discrete-time Markov
chains, Gambler's ruin problem,
Poisson processes, birth and death processes and other continuous Markov chains, renewal
reward processes. Martinagles, Brownian motion. Applications: queueing,
reliability, manufacturing, inventory, biology,
insurance risk, and financial engineering.
Prerequisites: a course(s) in probability (and some statistics)
(using calculus)
such as IEOR 4150 (Introduction to probability and statistics),
or Statistics GU4203 (Probability Theory), or Statistics GU4001
(Introduction to probability and statistics).
NO REQUIRED TEXT: Suggested but not required Text: Sheldon Ross Introduction to Probability Models, 10th/11th edition,
Academic Press, New York.
This course will cover the following topics in the context of operations research.
Lecture Notes (written by Professor Sigman)
will be posted on the course website covering the various topics.
- Review of probability
- Discrete-time Markov chains, Gambler's ruin problem
- Binomial Lattice Model for stocks, and the pricing of derivatives
- Introduction to point processes, renewal processes
- Exponential distribution and the Poisson process
- Renewal reward theorem
- Continuous-time Markov chains
- Martingales
- Introduction to Brownian motion with an application to financial engineering
- Brief Introduction to simulation (Time Permitting)