Department of Mathematics: Recent submissions
Now showing items 81-100 of 131
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Test of the overreaction hypothesis in the South African stock market
(University of the Western Cape, 2014)This research undertakes to investigate both long-term and short-term investor overreaction on the JSE Limited (JSE) over the period from 1 January 2002 to 31 December 2009. The period covers the restructuring and reform ... -
Investigating the difficulties of first year mainstream mathematics students at the University of the Western Cape with “related rates” problems
(University of the Western Cape, 2014)The aim of the thesis is to research the difficulties that first year mainstream mathematics students at UWC experience when solving Related Rates problems in calculus. In chapter 2, an in-depth study was made of the nature ... -
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 v-elements such that every pair of the elements of the set is contained in exactly one 3-subset. In this study, we discuss some ... -
The Birch and Swinnerton-Dyer Conjecture for elliptic curves.
(University of the Western Cape, 2014)The aim of this dissertation is to provide an exposition of the Birch and Swinnerton-Dyer 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 two-point 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 ... -
Efficient numerical methods based on integral transforms to solve option pricing problems
(University of the Western Cape, 2012)In this thesis, we design and implement a class of numerical methods (based on integral transforms) to solve PDEs for pricing a variety of financial derivatives. Our approach is based on spectral discretization of the ... -
Robust Spectral Methods for Solving Option Pricing Problems
(University of the Western Cape, 2012)Robust Spectral Methods for Solving Option Pricing Problems by Edson Pindza PhD thesis, Department of Mathematics and Applied Mathematics, Faculty of Natural Sciences, University of the Western Cape Ever since the ... -
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 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 ... -
Efficient numerical methods to solve some reaction-diffusion problems arising in biology
(2013)In this thesis, we solve some time-dependent partial differential equations, and systems of such equations, that governs reaction-diffusion models in biology. we design and implement some novel exponential time differencing ... -
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 ...