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# Mathematical Methods of Finance - MAT00020M

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• Department: Mathematics
• Module co-ordinator: Dr. Alet Roux
• Credit value: 20 credits
• Credit level: M
• Academic year of delivery: 2017-18

## Module will run

Occurrence Teaching cycle
A Autumn Term 2017-18

## Module aims

The topics covered are selected because of their importance in quantitative finance theory and practice. Probability theory and stochastic processes provide the language in which to express and solve mathematical problems in finance due to the inherent randomness of asset prices. The introduction of more advanced tools will be preceded by a brief review of basic probability theory with particular focus on conditional expectation. Then the module will proceed to present the theory of martingales and the study of three basic stochastic processes in finance: random walks, Brownian motion, and the Poisson process. An informal overview of Ito stochastic calculus will be given and first financial applications indicated. The material will be illustrated by numerous examples and computer-generated demonstrations. By the end of this module students are expected to achieve a sufficient level of competence in selected mathematical methods and techniques to facilitate further study of Mathematical Finance.

## Module learning outcomes

At the end of the module you should be able to:

use the language and tools of probability theory with confidence in the context of financial models and applications.

acquire an understanding of stochastic processes in discrete and continuous time and be familiar with the basic examples and properties of such processes appearing in financial modelling.

recognise the central role of Ito stochastic calculus for mathematical models in finance, and show familiarity with the basic notions and tools of stochastic calculus, at an informal level.

understand the notions of a parabolic partial differential equation and solutions to boundary/initial/final value problems, within the class of equations arising in typical problems in finance.

## Assessment

Task Length % of module mark
University - closed examination
Mathematical Methods of Finance
3 hours 100

None

### Reassessment

Task Length % of module mark
University - closed examination
Mathematical Methods of Finance
3 hours 100

## Module feedback

Individual feedback and advice on assessed coursework will be offered to students during scheduled office hours.