Ensimag Rubrique Formation 2022

Partial differential equations for finance - WMMFMA26

  • Number of hours

    • Lectures 12.0
    • Projects -
    • Tutorials -
    • Internship -
    • Laboratory works 6.0
    • Written tests -

    ECTS

    ECTS 2.0

Goal(s)

Know the different classes of Partial Differential Equations (PDEs): elliptic, parabolic, and hyperbolic. Understand their specific characteristics, particularly regarding the types of boundary conditions that must be considered. Understand what this implies for their numerical approximations. Applications to various PDE models arising in mathematical finance: Black-Scholes equation, Fokker-Planck equation, etc

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

Prerequisites

Mathematical analysis (normed spaces, elementary Fourier analysis), linear algebra, basic numerical methods.

Test

Evaluation : Examen Ecrit (2h)

Resit : Examen Ecrit (2h)

NORMAL SESSION :
Type of exam: written
Time: 2 hours
Documents authorized : None
Materials authorized, please specify : None

SECOND SESSION :
Type of exam: Written
Duration: 2 hours
Documents authorized: None
Material authorized, please specify : None

Calendar

The course exists in the following branches:

see the course schedule for 2025-2026

Additional Information

Course ID : WMMFMA26
Course language(s): FR

The course is attached to the following structures:

  • Team Finance.
  • Team Analysis-Computational Science

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)