Browsing Magister Scientiae - MSc (Mathematics and Applied Mathematics) by Title
Now showing items 58-77 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 ... -
Modelling the basel III capital adequacy and net stable funding ratios for a commercial bank following an optimal investment strategy
(University of the Western Cape, 2024)Commercial banks have a significant impact on a country’s economy as they raise capital, create liquidity by converting their customers’ deposits into loans, and deliver essential services such as loans, certificates of ... -
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. ... -
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 ... -
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 Xo of all finitely generated groups with finite commutator subgroups. We shall eventually narrow down to the groups of the form T)<lw zn for some nE N and some finite ... -
Numerical methods for the valuation of financial derivatives
(University of the Western Cape, 2005)Numerical methods form an important part of the pricing of financial derivatives and especially in cases where there is no closed form analytical formula. We begin our work with an introduction of the mathematical tools ... -
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. ... -
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 ... -
Numerical treatment of non-linear singular perturbation problems
(University of the Western Cape, 2007)This thesis deals with the design and implementation of some novel numerical methods for nonlinear singular perturbations problems (NSPPs). We provide a survey of asymptotic and numerical methods for some NSPPs in past ... -
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 ... -
On the method of lines for singularly perturbed partial differential equations
(University of the Western Cape, 2017)Many chemical and physical problems are mathematically described by partial differential equations (PDEs). These PDEs are often highly nonlinear and therefore have no closed form solutions. Thus, it is necessary to ... -
On the numerical integration of singularly perturbed Volterra integro-differential equations
(University of the Western Cape, 2017)Efficient numerical approaches for parameter dependent problems have been an inter- esting subject to numerical analysts and engineers over the past decades. This is due to the prominent role that these problems play in ... -
Pairings of Binary reflexive relational structures
(University of the Western Cape, 2008)The main purpose of this thesis is to study the interplay between relational structures and topology , and to portray pairings in terms of some finite poset models and order preserving maps. We show the interrelations ... -
Pairings of binary reflexive relational structures
(University of the Western Cape, 2007)The main purpose of this thesis is to study the interplay between relational structures and topology, and to portray pairings in terms of some finite poset models and order preserving maps. We show the interrelations between ... -
Pairings of binary reflexive relational structures
(University of the Western Cape, 2007)The main purpose of this thesis is to study the interplay between relational structures and topology, and to portray pairings in terms of some finite poset models and order preserving maps. We show the interrelations between ... -
The paradox of enrichment in predator-prey systems
(University of Western Cape, 2020)In principle, an enrichment of resources in predator-prey systems show prompts destabilisation of a framework, accordingly, falling trophic communication, a phenomenon known to as the \Paradox of Enrichment" [54]. After ... -
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 ... -
Pricing European options : a model-free approach
(University of the Western Cape, 2016)This paper focuses on the newly revived interest to model free approach in finance. Instead of postulating some probability measure it emerges in a form of an outer-measure. We review the behavior of a market stock price ... -
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 ... -
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 ...