Number of hours
- Lectures 12.0
- Projects -
- Tutorials -
- Internship -
- Laboratory works 6.0
- Written tests -
ECTS
ECTS 2.0
Goal(s)
Introduction to the different classes of partial differential equations: elliptic, parabolic and hyperbolic. Their characteristics and what this implies in terms of numerical approximations. Applications to various PDE models involved in mathematical finance. Among those, we will consider the Black-Scholes equation, Hamilton-Jacobi equations, in the framework of dynamic optimal control theory.
Responsible(s)
Olivier ZAHM
Content(s)
1. Introduction: origin of partial differential equations (PDE) in mathematical finance
2. Different types of partial differential equations: parabolic, elliptic, hyperbolic and of mixed type
What are the physical phenomenon associated to, and how do they appear in e.g. Black-Scholes equation (diffusion part, transport part).
3. Partial differential equations, initial and boundary conditions: how to set them?
Notion of characteristic surface for a PDE.
4. Hamilton-Jacobi equations and introduction to dynamic optimal control
5. Some elements of numerical analysis of PDEs: theory and practice
Mathematical analysis (normed spaces, elementary Fourier analysis), linear algebra, basic numerical methods.
Test
An exam at the end of the term (E).
- MCC en présentiel **
N1 = 1/2 TP encadré + 1/2 examen écrit
N2 = 1/2 TP encadré + 1/2 examen écrit
- MCC en présentiel **
- MCC en distanciel **
N1 = 1/2 TP à distance + 1/2 devoir à la maison
N2 = devoir à la maison
- MCC en distanciel **
Calendar
The course exists in the following branches:
- Curriculum - Financial Engineering - Semester 9
Additional Information
Course ID : WMMFMA26
Course language(s): 
The course is attached to the following structures:
- Team Analysis-Computational Science
- Team Finance.
You can find this course among all other courses.
Bibliography
L.C. Evans : Partial differential equations (AMS)
D.P. Bertsekas : Dynamic programming and optimal control (MIT)