- Docente: Paolo Foschi
- Credits: 6
- SSD: SECS-S/01
- Language: Italian
- Teaching Mode: Traditional lectures
- Campus: Rimini
- Corso: Second cycle degree programme (LM) in Statistical, Financial and Actuarial Sciences (cod. 6812)
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. (Prerequisite) Random variable, distributions, and convergence of random variables sequences.
* Ch. 1: da 1.1 a 1.6 included.
* Ch. 2: da 2.1 a 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, random walk and ruin probabilities.
* Ch. 8: 8.1, 8.2
* Ch. 9: 9.1, 9.5
* Ch. 3: 3.9, 3.10* Ch. 5: 5.3 3. Markov Chains
* Ch. 6: 6.1, 6.2, 6.3, 6.4 4.
4. The Poisson Process
* Ch. 6: 6.8 5.
5. Diffusion processes and Itô calculus:
* Ch. 13: 13.1, 13.2, 13.3, 13.7, 13.8, 13.9
Readings/Bibliography
Probability and Random Processes, G.R. Grimmett and D.R. Stirzaker, 4th Edition, Oxford university Press, 2020
Teaching methods
Classes and exercises
Assessment methods
A two-hours written examination that includes theoretical questions and exercises
Teaching tools
* Slides and lecture notes
* Solved exercises
* computer programs for the simulation of the presented random processes
Office hours
See the website of Paolo Foschi