# 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.