# ST339: Introduction to Mathematical Finance

**Lecturer(s): Dr Martin Herdegen**

**Prerequisites**:

- Students must have done either ST218 Mathematical Statistics A or ST220 Introduction to Mathematical Statistics.
- It is
*strongly**recommended*to take either MA359 Measure theory or ST342 Mathematics of Random Events alongside this module.

**Restrictions:**

- Statistics students may take
*at most one*of the following:- ST339 Introduction to Mathematical Finance
- EC333 Topics in Financial Economics: Theories and International Finance
- IB253 Principles of Finance 1

- Moreover, Statistics students who have taken ST339 Introduction to Mathematical Finance
*may not take*IB254 Principles of Finance 2.

**Commitment:**

- 3 hours of lectures per week. 5 example classes per term. This module runs in Term 1.

**Aims:**

- To provide an introduction to Mathematical Finance in discrete time and cover the discrete part of the CT8 actuarial syllabus.
- The Actuarial profession has agreed to grant an exemption to their professional examination CT8 to students who perform sufficiently well in the examinations
*for both*ST339 and ST401. - This module serves as a prerequisite for ST401, and for the following WBS finance modules:
- IB357 Investment Management
- IB359 Derivatives and Risk Management
- IB394 International Financial Management.

- It is also a prerequisite (acting as an alternative to EC333) for the module EC334 Topics in Financial Economics: Corporate Finance and Markets.

**Content:**

- Arbitrage theory
- Mean-variance portfolio selection and the Capital Asset Pricing Model
- Utility theory and Risk measures
- Pricing and Hedging in discrete time, Binomial Model

**Assessment: **100% by 2-hour exam in Summer.

**Illustrative Bibliography:**

- H. FĂ¶llmer and A. Schied:
*Stochastic Finance. An Introduction in Discrete Time*, 4th ed., de Gruyter, 2016. - S.F. LeRoy and J. Werner:
*Principles of Financial Economics*, 2nd ed., Cambridge University Press, 2014. - S.E. Shreve:
*Stochastic Calculus for Finance 1*: The Binomial Asset Pricing Model, Springer, 2003. - J. Jacod and P. Protter:
*Probability Essentials*, Springer, 2003.

Resources for current ST339 students via moodle (restricted access)