**Summary**

The course has been designed as an introduction to the mathematics needed for the study of financial derivatives. A number of subjects are introduced: Basic principles of topology and measure theory, functions of more than one variable and their derivatives, the Riemann Stieljes and Lebesque integrals, Fourier analysis, and partial differential equations.

**Module Information**

- 56847 378 (32) Financial Mathematics 378
- Year course in third year.
- Lecture load: 3 lectures, 3 tutorials per week.
- Prerequisite pass modules: Mathematics 214, 244 : prerequisite modules: Mathematical Statistics 214, 244.
- Language specification : A

**Lecturer**

- Dr P Ouwehand: Office 1018, Industrial Psychology/Mathematics Building (e-mail: peter_ouwehand@sun.ac.za)

**Study material
**

The prescribed text is:

*Probability Essentials*, by J. Jacod and P. Protter, Springer, 2004.

In addition, electronic notes will be provided.

**Module Content**

- Measure Theory, integration and probability theory
- Fourier analysis in Hilbert Space
- Stochastic calculus and stochastic differential equations
- Partial differential equations

**Opportunities for Learning**

- The material will be fully discussed in the lectures. In the tutorial periods the material of the lectures will be illustrated by examples and problems. The tutorials also offer an additional opportunity for further explanation.
- Teaching material will be made available on WebStudies.

**Assessment**

- Method: Earn classmark (CM40) and pass examination (FM50).
- The class mark is determined by your showing in three formal tests.
- Final Mark: FM = 0,4* class mark + 0,6* exam mark
- The dates and times of the tests are determined by the Faculty and appear in the Examination and Tests part of the University Year book. This Year book also contains further details of Examination and promotion regulations (Part 1 and 5 in particular).
- Final marks are made known on the dates as officially determined by the Year Program of the University. Students may discuss their examination papers with their lecturer, but only after the last day on which final marks may be handed in. (See Year Program) and before the passage of two months after this date.
- Attendance of tutorials is compulsory.

**Outcomes**

The Student who has passed this module should possess:

- A good understanding of the basic principles of topology and measure theory.
- A good understanding of how measure theory is used to construct probability theory.
- A basic facility with the handling of one-dimensional stochastic differential equations.
- A good background knowledge in (mainly) second order elliptic and parabolic PDEs.