Magister Scientiae  MSc (Mathematics and Applied Mathematics): Recent submissions
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Efficient Monte Carlo methods for pricing of electricity derivatives
(University of the Western Cape, 2012)We discuss efficient Monte Carlo methods for pricing of electricity derivatives. Electricity derivatives are risk management tools used in deregulated electricity markets. In the past,research in electricity derivatives ... 
Automorphism groups of some designs of steiner triple systems and the atomorphism groups of their block intersection graphs
(University of the Western Cape, 2014)A Steiner triple system of order v is a collection of subsets of size three from a set of velements such that every pair of the elements of the set is contained in exactly one 3subset. In this study, we discuss some ... 
The Birch and SwinnertonDyer Conjecture for elliptic curves.
(University of the Western Cape, 2014)The aim of this dissertation is to provide an exposition of the Birch and SwinnertonDyer Conjecture, considered by many to be one of the most important unsolved problems in modern Mathematics. A review of topics in Algebraic ... 
Mathematical model of performance measurement of defined contribution pension funds
(University of the Western Cape, 2015)The industry of pension funds has become one of the drivers of today’s economic activity by its important volume of contribution in the financial market and by creating wealth. The increasing importance that pension funds ... 
Numerical techniques for optimal investment consumption models
(University of the Western Cape, 2014)The problem of optimal investment has been extensively studied by numerous researchers in order to generalize the original framework. Those generalizations have been made in different directions and using different techniques. ... 
Multilevel Monte Carlo simulation in options pricing
(University of the Western Cape, 2014)In Monte Carlo path simulations, which are used extensively in computational finance, one is interested in the expected value of a quantity which is a functional of the solution to a stochastic differential equation [M.B. ... 
Mathematical modeling in the sustainable use of natural resources.
(University of the Western Cape, 2015)The sustainable use of natural resources is of utmost importance for every community. In particular, it is important for every given generation to plan in such a way that proper provision is made for future generations. ... 
On the design and implementation of a hybrid numerical method for singularly perturbed twopoint boundary value problems
(University of the Western Cape, 2014)With the development of technology seen in the last few decades, numerous solvers have been developed to provide adequate solutions to the problems that model different aspects of science and engineering. Quite often, these ... 
Codes Related to and Derived from Hamming Graphs
(University of the Western Cape, 2013)Codes Related to and Derived from Hamming Graphs T.R Muthivhi M.Sc thesis, Department of Mathematics, University of Western Cape For integers n; k 1; and k n; the graph k n has vertices the 2n vectors of Fn2 and ... 
Modelling of asset allocation in banking using the meanvariance approach
(University of the Western Cape, 2012)Bank asset management mainly involves profit maximization through invest ment in loans giving high returns on loans, investment in securities for reducing risk and providing liquidity needs. In particular, commercial ... 
Mathematical modeling and analysis of HIV/AIDS control measures
(University of the Western Cape, 2012)In this thesis, we investigate the HIV/AIDS epidemic in a population which experiences a significant flow of immigrants. We derive and analyse a math ematical model that describes the dynamics of HIV infection among the ... 
Preservice science teachers’ conceptual and procedural difficulties in solving mathematical problems in physical science
(University of the Western Cape, 2014)Students frequently leave firstyear physical science classes with a dual set of physical laws in mind the equations to be applied to qualitative problems and the entrenched set of concepts, many erroneous, to be applied ... 
Methods of optimizing investment portfolios
(2013)In this thesis, we discuss methods for optimising the expected rate of return of a portfolio with minimal risk. As part of the work we look at the Modern Portfolio Theory which tries to maximise the portfolio's expected ... 
A mathematical modeling of optimal vaccination strategies in epidemiology
(2010)We review a number of compartmental models in epidemiology which leads to a nonlinear system of ordinary differential equations. We focus an SIR, SEIR and SIS epidemic models with and without vaccination. A threshold ... 
Analysis and implementation of a positivity preserving numerical method for an HIV model
(2007)This thesis deals with analysis and implementation of a positivity preserving numerical method for a vaccination model for the transmission dynamics of two HIVsubtypesnin a given community. The continuous model is analyzed ... 
Discrete and continuous time methods of optimization in pension fund management
(2010)Pensions are essentially the only source of income for many retired workers. It is thus critical that the pension fund manager chooses the right type of plan for his/her workers.Every pension scheme follows its own set of ... 
Mathematical models of credit management and credit derivatives
(2010)The first two chapters give the background, history and overview of the dissertation, together with the necessary mathematical preliminaries. Thereafter, the next four chapters deal with credit risk and credit derivatives.The ... 
Pricing methods for Asian options
(2010)We present various methods of pricing Asian options. The methods include Monte Carlo simulations designed using control and antithetic variates, numerical solution of partial differential equation and using lower bounds.The ... 
Stochastic modelling in bank management and optimization of bank asset allocation
(2009)The Basel Committee published its proposals for a revised capital adequacy framework(the Basel II Capital Accord) in June 2006. One of the main objectives of this framework is to improve the incentives for stateoftheart ... 
Mathematical modelling of the HIV/AIDS epidemic and the effect of public health education
(University of Western Cape, 2014)HIV/AIDS is nowadays considered as the greatest public health disaster of modern time. Its progression has challenged the global population for decades. Through mathematical modelling, researchers have studied different ...