17266 - Stochastic Processes

Learning outcomes

The course deals with the basics of stochastic processes with applications in insurance and finance. At the end of the course the student is able to work with some of the most important kinds of random processes such as Markov chains, Poisson processes, birth and death processes and Brownian motion.

Course contents

1. (Pre-requisite) Random variables and probability distributions. Limit theorems for sequences of random variables.

• Ch. 1: §1.1 - §1.6 included.
• Ch. 2: §2.1 - §2.5 included
• Ch. 3: §3.1, 3.2, 3.3, 3.5, 3.6, 3.7.
• Ch. 4: §4.1, 4.2, 4.3, 4.5, 4.6.
• Ch. 7: §7.1, 7.2, 7.4, 7.5.

2. Introduction to random processes.

• Ch. 8: §8.1, 8.2
• Ch. 9: §9.1, 9.5

3. Random walks: risk processes and ruin probabilities.

• Ch. 3: §3.9, 3.10
• Ch. 5: §5.3

4. Markov chains

• Ch. 6: §6.1, 6.2, 6.3, 6.4

5. Poisson process
Ch. 6: §6.8

Readings/Bibliography

Textbook

• Probability and Random Processes, G.R. Grimmett and D.R. Stirzaker, 4th Edition, Oxford university Press, 2020.

Additional readings

• Elements of Applied Stochastic Processes, 3rd Edition U.N. Bhat, G.K. Miller, John Wiley & Sons, 2002.
• Stochastic Processes for Insurance and Finance, T. Rolski, H. Schmidli, V. Schmidt, J. Teugels, John Wiley & Sons, 2009.

Teaching methods

• Classes
• Exercises
  

Assessment methods

A two-hour written examination that includes

• theoretical questions
• exercises

Teaching tools

• Slides of the classes
• Solved exercises
  
• Past exams solved
  

Office hours

See the website of Simone Giannerini