Magister Scientiae - MSc (Mathematics and Applied Mathematics): Recent submissions
Now showing items 61-80 of 90
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Modelling of asset allocation in banking using the mean-variance 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 ... -
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 state-of-the-art ... -
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 ... -
Mathematical modeling of population dynamics of HIV with antiretroviral treatment and herbal medicine
(University of Western Cape, 2014)Herbal medicines have been an important part of health and wellness for hundreds of years. Recently the World Health Organization estimated that 80% of people worldwide rely on herbal medicines. Herbs contain many ... -
Discrete time methods of pricing Asian options
(University of Western Cape, 2014)This dissertation studies the computation methods of pricing of Asian options. Asian options are options in which the underlying variable is the average price over a period of time. Because of this, Asian options have a ... -
A mathematical modeling of optimal vaccination strategies in epidemiology
(University of the Western Cape, 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 ... -
A model of pension portfolios with salary and surplus process
(University of the Western Cape, 2010)Essentially this project report is a discussion of mathematical modelling in pension funds, presenting sections from Cairns, A.J.D., Blake, D., Dowd, K., Stochastic lifestyling: Optimal dynamic asset allocation for defined ... -
The non-cancellation groups of certain groups which are split extensions of a finite abelian group by a finite rank free abelian group
(University of the Western Cape, 2008)The groups we consider in this study belong to the class X0 of all nitely generated groups with nite commutator subgroups. We shall eventually narrow down to the groups of the form T owZn for some n 2 N and some nite ... -
Groupoids of homogeneous factorisations of graphs
(University of the Western Cape, 2009)This thesis is a study on the confluence of algebraic structures and graph theory. Its aim is to consider groupoids from factorisations of complete graphs. We are especially interested in the cases where the factors are ... -
Robust computational methods for two-parameter singular perturbation problems
(University of the Western Cape, 2010)This thesis is concerned with singularly perturbed two-parameter problems. We study a tted nite difference method as applied on two different meshes namely a piecewise mesh (of Shishkin type) and a graded mesh (of Bakhvalov ... -
A model for managing pension funds with benchmarking in an inflationary market
(University of the Western Cape, 2011)Aggressive fiscal and monetary policies by governments of countries and central banks in developed markets could somehow push inflation to some very high level in the long run. Due to the decreasing of pension fund benefits ... -
The influence of interfaces on the understanding of Mathematics in secondary schools in Afghanistan
(University of the Western Cape, 2010)The focus of this research is to establish whether there is a difference in the way the genders perceive the visualization of mathematics, with specific reference to set theory. The influence of the computing experience ... -
Numerical Treatment of Non-Linear singular pertubation problems
(University of the Western Cape, 2007)This thesis deals with the design and implementation of some novel numerical methods for non-linear singular pertubations problems (NSPPs). It provide a survey of asymptotic and numerical methods for some NSPPs in the past ...