This course introduces the theory and applications of several important stochastic processes. The course mainly includes Markov chains, Poisson process and Brownian motion. Students can also understand how to solve complicated problems using Monte Carlo simulation.

Course Materials

• Syllabus
• Lecture notes:
  • Chapter 0: Introduction
  • Chapter 1: Primer of statistics and probabilities
    • 1a: Probability and Random Variable
    • 1b: Expectation
    • 1c: Stochastic Process
    • 1d: Simulation
  • Chapter 2: Markov Chain
    • 2a: Transition Matrix and CK Equations
    • 2b: Classification of States
    • 2c: Branching Processes
  • Chapter 3: Counting Process
    • 3a: Poisson Process
    • 3b: Renewal Process
  • Chapter 4: Brownian Motion
    • 4a: Random Walk
    • 4b: Brownian Motion
    • 4c: Asset Returns
• R codes:
  • Distributions
  • Central limit theorem
• Assignments:
  • Assignment 1
    • Solution, R code
  • Assignment 2
    • Solution, R code

Course Outline

• Primer of statistics and probabilities
  • Introduction to probability theory
  • Random variables, expectations and conditioning
  • Simulations
• Markov chains
  • Discrete-time Markov chains
• Counting process
  • Poisson process
  • Renewal process
• Brownian motion
  • Random walks
  • Brownian motions

Grading

• Class participation: 10%
• Assignments: 25%
• Group project: 25%
• Thesis: 40%