2007/08 Taught Postgraduate Module Catalogue
MATH5360M Optimisation Methods for Finance
15 creditsClass Size: 100
Taught: Semester 2 (Jan to Jun) View Timetable
Year running 2007/08
This module is not approved as an Elective
Objectives
The aim of this module is to provide students with the analytical and numerical skills required to solve optimisation problems in finance. On completion of this module, students will be able to:- explain in detail convex sets and functions, constrained and unconstrained maximisation problems, global and local extrema;
- describe linear programming problems;
- demonstrate an understanding of Lagrange multipliers;
- solve linear programming problems numerically;
- optimise Value-at-Risk and conditional Value-at-Risk;
- describe quadratic programming problems;
- demonstrate an understanding of numerical algorithms for solving quadratic programming problems;
- solve mean-variance optimisation problems;
- demonstrate an understanding of simple stochastic programming problems;
- solve simple asset-liability management problems;
- apply optimisation methods in risk management.
Syllabus
Portfolio choice, risk management and pricing of financial derivatives require solving optimisation problems. This module will develop the relevant mathematical tools and numerical methods for analysing optimisation problems in finance. The students will acquire the necessary analytical and programming skills to solve maximisation problems and financial optimisation tasks.
The module covers linear, quadratic and stochastic programming. Practical applications include arbitrage-free pricing of options, optimisation of Value-at-Risk and conditional Value-at-Risk, calculation of mean-variance optimal portfolios, estimation of the efficient frontier, applications to asset-liability management and risk management.
On completion of this module the student will be familiar with linear and quadratic optimisation problems and have a basic understanding of stochastic programming problems. The student will be able to apply these mathematical techniques to solve realistic financial optimisation problems in portfolio and risk management.
Teaching methods
| Delivery type | Number | Length hours | Student hours |
| Lecture | 5 | 4.00 | 20.00 |
| Practical | 5 | 1.00 | 5.00 |
| Tutorial | 5 | 1.00 | 5.00 |
| Private study hours | 120.00 | ||
| Total Contact hours | 30.00 | ||
| Total hours (100hr per 10 credits) | 150.00 | ||
Private study
12 hours per lecture: 60 hours;4 hours per tutorial: 20 hours;
4 hours per practical class: 20 hours;
Preparation for assessment: 20 hours.
Opportunities for Formative Feedback
This module is taught en-bloc. Progress will be monitored by contributions made to tutorials and classes.Methods of assessment
Coursework
| Assessment type | Notes | % of formal assessment |
| Report | Take home exam in the form of 1 x 2,000 word written report | 100.00 |
| Total percentage (Assessment Coursework) | 100.00 | |
Normally resits will be assessed by the same methodology as the first attempt, unless otherwise stated
Reading list
The reading list is available from the Library websiteLast updated: 24/05/2010
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