> Formation > Cursus ingénieur
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.
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.
An exam at the end of the term (E).
The course exists in the following branches:
Course ID : WMMFMA26
Course language(s):
The course is attached to the following structures:
You can find this course among all other courses.
L.C. Evans : Partial differential equations (AMS)
D.P. Bertsekas : Dynamic programming and optimal control (MIT)
Date of update September 21, 2022
Nos sites
e-Services
