Prerequisite knowledge

The only prerequisite module for Mathematical Finance III is Probability II. This document contains an outline of the topics from Probability II that we’ll be using most often, and that you should have a good working knowledge of before we start.

If you have two hours

If you have two hours to spend preparing for Mathematical Finance III, I suggest you read the notes below, and also brush up on the following sections from Probability II. You should be able to:

define and work with probability spaces, including \(\sigma\)-algebras and their properties (Section 1.1)
use random variables when they are defined as functions on the probability space (Section 1.3)
work with the different modes of convergence of sequences of random variables: remember their definitions, and how the different types of convergence connect to each other (Sections 3.2 and 3.4).

If you have longer

If you have longer than two hours or want some extra practice, you might also like to try some exercises from each of these sections: I suggest

1.1 and 1.2
1.20
3.52 and 3.60

(numbers refer to this year’s Prob II problems sheet)

If you only do one thing

If you only do one thing to prepare for Mathematical Finance, look through the next section, which contains notes on “probability revision” produced by Andrew Wade. They cover some of the basics of probability which you should have seen in your first and second years at Durham.