MA908-15 Partial Differential Equations in Finance
Introductory description
N/A.
Module aims
To provide both a theoretical and a practical understanding of partial differential equations, including numerical methods. To link the above with problems from Finance. To give an introduction into optimal control.
Outline syllabus
This is an indicative module outline only to give an indication of the sort of topics that may be covered. Actual sessions held may differ.
Basic Theory of first and second order scalar linear PDEs (parabolic, elliptic, hyperbolic), basic properties, the role of boundary conditions, explicit solutions, Fourier series.
Examples of PDE in finance: Black-Scholes PDE, Kolmogorov equations, Hamilton-Jacobi-Bellman.
Optimal control HJB equation, comparison principles, stochastic optimal control. Example: optimal consumption.
Numerics of PDE: consistency, stability, convergence, discretisation.
Example: Crank-Nicolson.
Learning outcomes
By the end of the module, students should be able to:
- Understand three different types of partial differential and the appropriate boundary conditions.
- Understand the link between Optimal Control and the Hamilton-Jacobi-Bellman equation.
- Derive finite-difference formulae for a variety of differential operators on a variety of meshes and obtain the order of accuracy of the approximations.
- Obtain stability limits for numerical schemes.
- Demonstrate analytical skills and critical thinking.
Subject specific skills
Be able to choose appropriate partial differential equations for option pricing problems.
Transferable skills
Students will acquire key reasoning and problem solving skills which will empower them to address new problems with confidence.
Study time
| Type | Required |
|---|---|
| Lectures | 9 sessions of 2 hours (12%) |
| Seminars | 9 sessions of 1 hour (6%) |
| Private study | 123 hours (82%) |
| Total | 150 hours |
Private study description
Review lectured material and work on set exercises.
Costs
No further costs have been identified for this module.
You do not need to pass all assessment components to pass the module.
Students can register for this module without taking any assessment.
Assessment group D1
| Weighting | Study time | Eligible for self-certification | |
|---|---|---|---|
Assessment component |
|||
| In-class test | 15% | No | |
Reassessment component is the same |
|||
Assessment component |
|||
| In-Person Examination | 85% | No | |
|
|||
Reassessment component is the same |
|||
Feedback on assessment
Exam feedback.
Courses
This module is Optional for:
- Year 1 of TIBS-N3G1 Postgraduate Taught Financial Mathematics