Special Mathematics Lecture (Introduction to stochastic calculus)

Goals of the Course

Mathematics play a central role in all natural and social sciences. It is a universal language which can be learned, enjoyed, and shared by everybody. The goal of this course is to provide a solid knowledge on various mathematical topics. Each semester, a new subject is proposed, and the presentation is accessible to all motivated students, independently of their major and of their academic age. These lectures also offer a unique opportunity to study in an international, transdisciplinary, and friendly environment.

Objectives of the Course

The aim of this course is to understand the mathematics behind the Brownian motion and behind the Black-Scholes model. Other applications will be studied depending on the interest of the audience.

Course Contents or Plan

1. Mathematical Background
2. Gaussian processes
3. Brownian motion
4. Stochastic integrals
5. Itô processes and stochastic differential equations
6. Markov processes
7. Applications to finance

Course Prerequisites and Related Courses

Basic knowledge on calculus and linear algebra, as provided in Calculus I & II and in Linear algebra I & II. Motivated 1st year students can also attend without these prerequisites but after a discussion with the instructor.

Course Evaluation Method and Criteria

The final grade will be based on the active participation during the lectures and on some written reports. Students will be encouraged to work on applications related to their major during the semester. Students need to notify the course withdrawal to the instructor when they have no intention of finishing the course during the semester.

Study Load (Self-directed Learning Outside Course Hours)

Students are expected to read their notes, and to be familiar with the content of the previous lectures before each new lecture.

Notice for students

It is expected that the students will show a certain maturity in studying independently and in choosing some exercises and problems to solve. Study sessions will be organized on a weekly basis.

Textbook

Lecture Notes

Additional information

Reference Website

This lecture is provided under Creative Commons Attribution-Non Commercial-ShareAlike 4.0 International.