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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 ...
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 ...
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 ...
Construction and analysis of efficient numerical methods to solve mathematical models of TB and HIV co-infection
(University of the Western Cape, 2011)
The global impact of the converging dual epidemics of tuberculosis (TB) and human immunodeficiency virus (HIV) is one of the major public health challenges of our time, because in many countries, human immunodeficiency ...
Strong simplicity of groups and vertex - transitive graphs
(University of the Western Cape, 2010)
In the course of exploring various symmetries of vertex-transitive graphs, we introduce the concept of quasi-normal subgroups in groups. This is done since the symmetries of vertex-transitive graphs are intimately linked ...
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 ...
Pricing American style employee stock options having GARCH effects
(University of the Western Cape, 2010)
We investigate some simulation-based approaches for the valuing of the employee stock options. The mathematical models that deal with valuation of such options include the work of Jennergren and Naeslund [L.P Jennergren ...