# 2018/19 Taught Postgraduate Module Catalogue

## MATH5360M Optimisation Methods for Finance

### 15 creditsClass Size: 70

Module manager: Dr Graham Murphy; Dr James Fung
Email: G.J.Murphy@leeds.ac.uk; J.C.L.Fung@leeds.ac.uk

Taught: Semester 1 View Timetable

Year running 2018/19

### Pre-requisite qualifications

The qualifications to gain entrance to the MSc in Financial Mathematics are sufficient.

This module is not approved as an Elective

### Objectives

To provide students with the analytical and numerical skills required to solve optimisation and derivative pricing problems in finance.

Learning outcomes
On completion of this module, students will be able to:
- write algorithms for solution of mathematical and finance related tasks;
- write simple programmes for solution of mathematical and finance-related tasks;
- 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;
- describe quadratic programming problems;
- demonstrate an understanding of numerical algorithms forsolving 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.

Skills outcomes
Computer programming, algorithms, numerics, optimisation techniques, applications in portfolio and risk management

### Syllabus

Portfolio choice, risk management and pricing of financial derivatives require solving optimisation problems. The module will develop the relevant mathematical tools, numerical methods and programming skills for analysing and solving optimisation problems in finance.

The module covers linear, quadratic and stochastic programming. Practical applications include arbitrage-free pricing of options, optimisation of risk measures, calculation of optimal portfolios, applications to asset-liability management and risk management. The module provides an introduction to a programming language.

### Teaching methods

 Delivery type Number Length hours Student hours Lecture 10 2.00 20.00 Practical 10 1.00 10.00 Seminar 10 1.00 10.00 Private study hours 110.00 Total Contact hours 40.00 Total hours (100hr per 10 credits) 150.00

### Private study

4 hours per lecture
2 hours per tutorial
1 hours per practical

40 hours Preparation for assessment

### Opportunities for Formative Feedback

Progress will be monitored by contributions made to tutorials and during practicals; performance in ACWs.

### Methods of assessment

Coursework
 Assessment type Notes % of formal assessment In-course Assessment . 40.00 Total percentage (Assessment Coursework) 40.00

The resit for this module will be 100% by 2 hours examination

Exams
 Exam type Exam duration % of formal assessment Standard exam (closed essays, MCQs etc) 2 hr 60.00 Total percentage (Assessment Exams) 60.00

The resit for this module will be 100% by 2 hours examination.