Calcul stochastique

See the French version for more details.
The content of this course is the introduction of concepts related to Brownian motion, stochastic integration, stochastic differential equations and a link with PDE's and the change of probability measures. In particular, we will derive Ito's lemma, the theorem of Girsanov and the lemma of Feynman-Kac. 

See the French version for more details.
The purpose of this course is to provide the necessary background for enabling the student to understand and employ the basic concepts of the theory.

Required and Corequired knowledge and skills

Probability theory, martingale theory and stochastic processes in general.

Theoretical lectures.
There will be some small exercises and examples.
 

Contribution to the teaching profile

See the French version for more details.
In general, stochastic calculus is a subfield of mathematics at the interplay of probability theory, stochastic processes and real analysis. The core theme is to define and analyze the properties of a "stochastic integral", that means an integral in which the integrand and the integrator are allowed to be stochastic processes. Stochastic finance is one of the most prominent areas of application, where it plays a fundamental role for the pricing and hedging of financial derivatives. 

References, bibliography, and recommended reading

Steele J. Michael, 2001, " Stochastic Calculus and Financial Applications ", Springer-Verlag, Applications of Mathematics.

Course notes

• Université virtuelle

Contacts

Griselda Deelstra (Campus de la Plaine, room O.9.110)

Campus

Plaine

Method(s) of evaluation

• Oral examination

Oral examination

The assessment method could be adapted according to the sanitary situation.

Mark calculation method (including weighting of intermediary marks)

The mark is completely based on the exam.

Language(s) of evaluation

• french