IB3K215 Financial Optimisation
Introductory description
N/A.
Module aims
The module aims to introduce modelling and solving approaches for mathematical programming problems arising in finance. The optimization methods such as linear, integer, dynamic, nonlinear and stochastic programming will be motivated through practical financial decision making problems. The main topics to be covered in Financial Optimisation include asset allocation, portfolio optimisation, risk management, asset/liability cashflow matching, and option pricing and hedging. A modelling language AMPL using different commercial solvers for financial decisionmaking problems will be introduced.
Outline syllabus
This is an indicative module outline only to give an indication of the sort of topics that may be covered. Actual sessions held may differ.
 Revision (linear algebra, calculus and optimisation).
 Introduction to AMPL: modelling and solving optimization problems.
 Linear programming: dedication and cash flow matching.
 Duality: applications to asset pricing, option pricing and arbitrage detection.
 Quadratic programming: meanvariance portfolio optimization.
 Nonlinear programming: parameter estimation in portfolio optimization, robust assset allocation.
 Modelling with discrete decisions: constructing an index fund.
 Dynamic optimization for fixedincome securities.
 Stochastic programming: asset and liability management, corporate debt management, robust asset allocation.
 Scenario optimization: meanabsolute deviation models, risk management (Conditional ValueatRisk).
Learning outcomes
By the end of the module, students should be able to:
 Define concepts and optimisation methods commonly used in finance.
 Use a range of techniques to solve typical financial optimisation problems.
 Understand the particular challenges of modelling and solving financial optimisation problems.
 Identify appropriate methods for financial optimisation problems.
 Determine the strengths and weaknesses of different approaches.
 Analyse case studies and model the underlying problems properly.
Indicative reading list
 S. A. Zenios, Practical Financial Optimization: Decision Making for Financial Engineers, John Wiley & Sons, 2008.
 G. Cornuejols and R. Tutuncu, Optimization Methods in Finance, Cambridge University Press, 2007.
 W. T. Ziemba and R. G. Vickson, Stochastic Optimization Models in Finance, World Scientific, 2006.
 G. Cornuejols and R. Tutuncu, Optimization Methods in Finance, Cambridge University Press, 2007.
 F. Fabozzi, P. Kolm, D. Pachamanova, S. Focardi, Robust Portfolio Optimization and Management, John Wiley & Sons, 2007.
 D. G. Luenberger, Investment Science, 2nd Edition, Oxford University Press, 2013.
Subject specific skills
Use AMPL to model decision making problems in finance.
Apply bultin/addon solvers to solve optimisation problems.
Transferable skills
Distinguish between different modelling and solution approaches for finance problems.
Study time
Type  Required 

Lectures  10 sessions of 1 hour (7%) 
Tutorials  10 sessions of 1 hour (7%) 
Online learning (independent)  10 sessions of 1 hour (7%) 
Private study  48 hours (32%) 
Assessment  72 hours (48%) 
Total  150 hours 
Private study description
Private Study.
Costs
No further costs have been identified for this module.
You do not need to pass all assessment components to pass the module.
Assessment group D3
Weighting  Study time  

Quiz Work  10%  7 hours 
Quiz work (scores from the nine/ten weekly quizzes would be added up and the percentage of the whole would be given as this score). 

Individual Assignment (15 CATS)  20%  14 hours 
The written assessment is based on problem solving. The number of questions will vary from 2 to 4 related to subjects to be covered in the module. Depending on the complexity of real cases and their application areas, each question may have several parts. Accordingly the page limit will vary from 5 to 8 pages. A supplementary document can be used for presenting data, intermediate calculations and/or computer codes if necessary. 

Online Examination  70%  51 hours 
Exam ~Platforms  AEP

Feedback on assessment
Feedback via my.wbs.
Prerequisites
Students are required to have basic knowledge on modelling and solving linear (and/or integer) programming problems.
To take this module, you must have passed:
Courses
This module is Optional for:

USTAG300 Undergraduate Master of Mathematics,Operational Research,Statistics and Economics
 Year 3 of G300 Mathematics, Operational Research, Statistics and Economics
 Year 4 of G300 Mathematics, Operational Research, Statistics and Economics

USTAG1G3 Undergraduate Mathematics and Statistics (BSc MMathStat)
 Year 3 of G1G3 Mathematics and Statistics (BSc MMathStat)
 Year 4 of G1G3 Mathematics and Statistics (BSc MMathStat)

USTAG1G4 Undergraduate Mathematics and Statistics (BSc MMathStat) (with Intercalated Year)
 Year 4 of G1G4 Mathematics and Statistics (BSc MMathStat) (with Intercalated Year)
 Year 5 of G1G4 Mathematics and Statistics (BSc MMathStat) (with Intercalated Year)
This module is Unusual option for:

UPHAV7ML Undergraduate Philosophy, Politics and Economics
 Year 3 of V7ML Philosophy, Politics and Economics (Tripartite)
 Year 3 of V7ML Philosophy, Politics and Economics (Tripartite)
 Year 3 of V7ML Philosophy, Politics and Economics (Tripartite)
This module is Option list A for:
 Year 3 of USTAG300 Undergraduate Master of Mathematics,Operational Research,Statistics and Economics

USTAG301 Undergraduate Master of Mathematics,Operational Research,Statistics and Economics (with Intercalated
 Year 3 of G30E Master of Maths, Op.Res, Stats & Economics (Actuarial and Financial Mathematics Stream) Int
 Year 3 of G30E Master of Maths, Op.Res, Stats & Economics (Actuarial and Financial Mathematics Stream) Int
 Year 4 of G30E Master of Maths, Op.Res, Stats & Economics (Actuarial and Financial Mathematics Stream) Int

USTAY602 Undergraduate Mathematics,Operational Research,Statistics and Economics
 Year 3 of Y602 Mathematics,Operational Research,Stats,Economics
 Year 3 of Y602 Mathematics,Operational Research,Stats,Economics
This module is Option list B for:

USTAGG14 Undergraduate Mathematics and Statistics (BSc)
 Year 3 of GG14 Mathematics and Statistics
 Year 3 of GG14 Mathematics and Statistics
 Year 4 of USTAGG17 Undergraduate Mathematics and Statistics (with Intercalated Year)
This module is Option list C for:

USTAG300 Undergraduate Master of Mathematics,Operational Research,Statistics and Economics
 Year 4 of G30C Master of Maths, Op.Res, Stats & Economics (Operational Research and Statistics Stream)
 Year 4 of G30C Master of Maths, Op.Res, Stats & Economics (Operational Research and Statistics Stream)
 Year 5 of USTAG301 Undergraduate Master of Mathematics,Operational Research,Statistics and Economics (with Intercalated
This module is Option list D for:

USTAG300 Undergraduate Master of Mathematics,Operational Research,Statistics and Economics
 Year 3 of G30C Master of Maths, Op.Res, Stats & Economics (Operational Research and Statistics Stream)
 Year 3 of G30C Master of Maths, Op.Res, Stats & Economics (Operational Research and Statistics Stream)

USTAG301 Undergraduate Master of Mathematics,Operational Research,Statistics and Economics (with Intercalated
 Year 3 of G30G Master of Maths, Op.Res, Stats & Economics (Operational Research and Statistics Stream) Int
 Year 4 of G30G Master of Maths, Op.Res, Stats & Economics (Operational Research and Statistics Stream) Int
This module is Option list G for:

UPHAV7ML Undergraduate Philosophy, Politics and Economics
 Year 2 of V7ML Philosophy, Politics and Economics (Tripartite)
 Year 2 of V7ML Philosophy, Politics and Economics (Tripartite)
 Year 2 of V7ML Philosophy, Politics and Economics (Tripartite)