07s-08
PROBABILITY THEORY

Arturo KOHATSU-HIGA (School of Engineering Science)

Objective
  This course introduces basic elements of Probability Theory for use in various applications. In particular, we will concentrate on some related aspects of Monte Carlo simulation methods and Mathematical Finance.

Course Schedule
  1. Elements of Probability.
    Types of Distributions. Probability Mass Functions.
    Probability Density Functions.
    Dependence and Independence of Random Variables.
    Statistical Measures of Expectation, Variation, and Risk.
  2. Random Numbers
  3. Generating Discrete and Continuous Random Variables
  5. Geometric Brownian motion
  6. Interest rates and present value analysis
  7. Pricing contracts via Arbitrage
  8. The Arbitrage Theorem
  9. The Black-Scholes formula
  10. Variance Reduction Techniques

Prerequisites
  A basic multivariate calculus course. In particular we will use integration theory.

References
  The course will be based on the following textbooks.
  1. An Elementary Introduction to Mathematical Finance Options and other Topics 2nd Edition
  Sheldon M. Ross University of California, Berkeley
  2. An elementary introduction to mathematical finance: options and other topics. 2nd edition. Sheldon M. Ross. Cambridge: Cambridge University Press 2003
  Basic rules: Students are expected to read the textbook in advance and attend all lectures and to participate actively in them.

Evaluation
  The final grade will be mostly based on a final exam which will be centered on the theoretical aspects discussed in class. Some credit will be given for class participation, project development and problem solutions. Projects and problems will be proposed by the instructor through his webpage. A teaching assistant will be in charge of assisting the students to help them with these duties,

Teaching Aids
  The course will be complemented with various experiments, learning sites and problems proposals that will appear in the webpage of the instructor.