MATH-431 / 5 crédits

Enseignant: Wang Zhe

Langue: Anglais

## Summary

Introduction to the mathematical theory of stochastic calculus: construction of stochastic Ito integral, proof of Ito formula, introduction to stochastic differential equations, Girsanov theorem and Feynman-Kac formula.

## Keywords

stochastic calculus, Ito's integral, stochastic differential equations, Girsanov theorem, Feynman-Kac formula

## Required courses

• Bachelor programme of the Mathematics section
• Swiss school programme up to "Maturité"

## Important concepts to start the course

Advanced Probability, Probability and analysis course in the Bachelor programme of the Mathematics section

## Learning Outcomes

By the end of the course, the student must be able to:

• Demonstrate mastery of the course material
• Demonstrate mastery of the problems related to the exercices sessions
• Demonstrate mastery of the prerequisites
• Demonstrate the capability of using these notions in other contexts

## Transversal skills

• Use a work methodology appropriate to the task.

## Teaching methods

Ex lecture and exercises

## Expected student activities

Attend lecture regularly, solve the exercises and write down the solutions, study the previous course material before the next course, go over the material before the exam.

## Assessment methods

Written exam

In the case of Article 3 paragraph 5 of the Section Regulations, the teacher decides on the form of the examination he communicates to the students concerned.

No

## Bibliography

• J. Michael Steele, Stochastic Calculus and Financial Applications. Springer (2001)
• B. Oksendal, Stochastic Differential Equations (6th edition). Springer (2003)

## Prerequisite for

• martingales in financial mathematics
• stochastic control

## Dans les plans d'études

• Semestre: Automne
• Forme de l'examen: Ecrit (session d'hiver)
• Matière examinée: Theory of stochastic calculus
• Cours: 2 Heure(s) hebdo x 14 semaines
• Exercices: 2 Heure(s) hebdo x 14 semaines
• Semestre: Automne
• Forme de l'examen: Ecrit (session d'hiver)
• Matière examinée: Theory of stochastic calculus
• Cours: 2 Heure(s) hebdo x 14 semaines
• Exercices: 2 Heure(s) hebdo x 14 semaines
• Semestre: Automne
• Forme de l'examen: Ecrit (session d'hiver)
• Matière examinée: Theory of stochastic calculus
• Cours: 2 Heure(s) hebdo x 14 semaines
• Exercices: 2 Heure(s) hebdo x 14 semaines
• Semestre: Automne
• Forme de l'examen: Ecrit (session d'hiver)
• Matière examinée: Theory of stochastic calculus
• Cours: 2 Heure(s) hebdo x 14 semaines
• Exercices: 2 Heure(s) hebdo x 14 semaines

## Semaine de référence

 Lu Ma Me Je Ve 8-9 9-10 10-11 11-12 12-13 13-14 CO121 14-15 15-16 CO121 16-17 17-18 18-19 19-20 20-21 21-22

Lundi, 13h - 15h: Cours CO121

Lundi, 15h - 17h: Exercice, TP CO121