Mat-1.3980 Stochastic Simulation, 3+2 cr.
| Exam: January 12th, 2007 from 12-15 @U358.
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| Project's deadline: January 29th, 2007 at 12:00 am.
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Teacher:
Lecturer: Visiting Professor
Karl Sigman
Assistant: Igor
Morlanes
Prerequisites:
Students need to have a background in (non-measure theoretic)
Probability Theory
at the level of (say) S. Ross, "A first course in probability", basic
statistics (confidence intervals, sampling,
strong law of large numbers and the central limit theorem).
Knowledge of stochastic processes (Markov chains, Poisson process) is
helpful (such as at the level of S. Ross,
"An Introduction to probability models"). They also need to use a software
such as MATLAB, or if they wish a high level language such as C++.
Syllabus:
- Random number generators: Pseudo-random uniform numbers,
statistical tests for generators
- Random variate generation: inverse transform method in both the
discrete and continuous case.
Generating from specific distributions; the Bernoulli, binomial,
exponential, Weibull for example.
- Monte Carlo simulation, an introduction: Evaluating integrals and
expected values;
examples from queueing
(telecommunications, manufacturing), finance (option pricing), etc.
- General discrete event simulation: Long-run simulations and
"steady-state", finite horizon simulations with a re-look at Monte Carlo.
- Further methods in random variate generation:
Composition method, acceptance rejection method.
- Normal distribution generation; polar and other methods.
Application to stock pricing in continuous time (Brownian motion,
geometric Brownian motion; Black-Scholes).
- Output analysis: variance reduction methods; antithetic
variables, common random numbers, conditioning, etc.
Schedule:
The course will be lectured during the second teaching period
from November 14th till December 13th of 2006.
- The lectures will be every Tuesday from 10-12 @U322 and from 14-16 @Y427b.
- The last one will be on Wednesday 13th from 10-12 @Y227 and from 13-15 @U262.
Literature:
Suggested Text : S. Ross (2006) (4th Edition). Simulation.
Academic Press, N.Y.
Suggested Reference Texts :
A. Law and W. Kelton (3rd Edition).
Simulation Modeling and Analysis.
McGraw-Hill, Inc. N.Y.