Financial Mathematics BSc

You will explore the concepts of discrete time Markov chains to understand how they used. We will also provide an introduction to probabilistic and stochastic modelling of investment strategies, and for the pricing of financial derivatives in risky markets.

You will gain well-rounded knowledge of contemporary issues which are of importance in research and workplace applications.

This module involves the application of mathematics to a variety of practical, open-ended problems - typical of those that mathematicians encounter in industry and commerce.

Specific projects are tackled through workshops and student-led group activities. The real-life nature of the problems requires you to develop skills in model development and refinement, report writing and teamwork. There are various streams within the module, for example:

• Pure Mathematics
• Applied Mathematics
• Data Analysis
• Mathematical Physics

This ensures that you can work in the area that you find most interesting.

This course provides an introduction to coding theory in particular to error-correcting codes and their uses and applications. It also provides an introduction to to cryptography, including classical mono and polyalphabetic ciphers as well as modern public key cryptography and digital signatures, their uses and applications.

This course provides an opportunity for third-year students to gain first-hand experience of being involved with providing mathematical education. Students will work at local schools alongside practising mathematics teachers in a classroom environment and will improve their skills at communicating mathematics. Typically, each student will work with a class (or classes) for half a day a week for about sixteen weeks. Students will be given a range of responsibilities from classroom assistant to leading a self-originated mathematical activity or project. The assessment is carried out by a variety of means: on-going reflective log, contribution to reflective seminar, oral presentation and a final written report.

This module will offer an introduction to some theoretical concepts related to the allocation of risk by financial institutions. Then it will apply these concepts to the analysis of financial and banking crises.

This module examines the workings of the major financial markets. Markets for equity and debt are dealt with (money and foreign exchange markets are also the focus) as are markets for derivative instruments. The module covers the key theoretical models of modern finance, key market conventions and mechanisms, financial risk management with derivative instruments.

Game theory contains many branches of mathematics (and computing); the emphasis here is primarily algorithmic. The module starts with an investigation into normal-form games, including strategic dominance, Nash equilibria, and the Prisoner’s Dilemma. We look at tree-searching, including alpha-beta pruning, the ‘killer’ heuristic and its relatives. It then turns to mathematical theory of games; exploring the connection between numbers and games, including Sprague-Grundy theory and the reduction of impartial games to Nim.

This module discusses and analyses the management of the international finance function of firms. Typical issues include:

• foreign exchange markets
• foreign exchange and other international risks
• international financial markets
• international investment decisions
• foreign trade 

In this module a variety of techniques and areas of mathematical optimisation will be covered including Lagrangian methods for optimisation, simplex algorithm linear programming and dynamic programming. You’ll develop techniques for application which can be used outside the mathematical arena. 

20 credits in the Autumn Semester.

This module examines individual decision-making under conditions of risk and uncertainty, and investigates the effectiveness of insurance as a means of controlling risk.

This module will introduce the different aspects of corporate risk and examine how the risk of fortuitous loss may affect the various stakeholders in the operations of firms.

This module will discuss the processes utilised by corporate enterprises to manage the risk of fortuitous loss. Once corporate risks have been identified and their impact on the firm measured, risk management attempts to control the size and frequency of loss, and to finance those fortuitous losses which do occur. 

You'll learn how to use numerical techniques for determining the approximate solution of ordinary and partial differential equations where a solution cannot be found through analytical methods alone. You will also cover topics in numerical linear algebra, discovering how to solve very large systems of equations and find their eigenvalues and eigenvectors using a computer.

This course is concerned with the two main theories of statistical inference, namely classical (frequentist) inference and Bayesian inference. The classical inference component of the module builds on the ideas of mathematical statistics introduced in MATH2011. Topics such as sufficiency, estimating equations, likelihood ratio tests and best-unbiased estimators are explored in detail. There is special emphasis on the exponential family of distributions, which includes many standard distributions such as the normal, Poisson, binomial and gamma.

In Bayesian inference, there are three basic ingredients: a prior distribution, a likelihood and a posterior distribution, which are linked by Bayes' theorem. Inference is based on the posterior distribution, and topics including conjugacy, vague prior knowledge, marginal and predictive inference, normal inverse gamma inference, and categorical data are pursued. Common concepts, such as likelihood and sufficiency, are used to link and contrast the two approaches to inference. Students will gain experience of the theory and concepts underlying much contemporary research in statistical inference and methodology. Students will gain experience of using statistical software and interpreting its output.

This module will develop your knowledge of discrete-time Markov chains by applying them to a range of stochastic models. You will be introduced to Poisson and birth-and-death processes. You will then move onto more extensive studies of epidemic models and queuing models, with introductions to component and system reliability.

This module will provide a general introduction to the analysis of data that arise sequentially in time. Several commonly occurring models will be discussed and their properties derived. Methods for model identification for real time series data will be described. Techniques for estimating the parameters of a model, assessing its fit and forecasting future values will be developed. You will gain experience of using a statistical package and interpreting its output.