Course teacher(s)
Griselda DEELSTRA (Coordinator)ECTS credits
5
Language(s) of instruction
french
Course content
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. Several applications in stochastic finance will be discussed.
Objectives (and/or specific learning outcomes)
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.
Teaching methods and learning activities
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
Other information
Contacts
Griselda Deelstra (Campus de la Plaine, room O.9.110)
Campus
Plaine
Evaluation
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