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Analysis and simulation of nonlinear option pricing problems
(University of Western Cape, 2021)
We present the Black-Scholes Merton partial differential equation (BSMPDE) and its
analytical solution. We present the Black-Scholes option pricing model and list some
limitations of this model. We also present a nonlinear ...
Model theory of algebraically closed fields and the Ax-Grothendieck Theorem
(University of Western Cape, 2020)
We introduce the concept of an algebraically closed field with emphasis of the basic model-theoretic
results concerning the theory of algebraically closed fields. One of these nice results about algebraically
closed ...
Estimating the cost of deposit insurance for a commercial bank following an optimal investment strategy
(University of Western Cape, 2020)
Commercial banks play a dominant role in facilitating the economic growth of a country by acting
as an intermediary between the de cit spending unit (borrowers) and the surplus spending
unit (lenders). In particular, ...
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 ...
Ultrafilters and Compactification
(UWC, 2020)
In this thesis, we construct the ultrafilter space of a topological space using ultrafilters as points, study some of its properties and describe a method of generating compactifications through the ultrafilter space. As ...
Mathematical modeling of the population dynamics and optimal control of COVID-19 disease
(2024)
Since the onset of the COVID-19 pandemic, researchers speculated that this virus would create numerous challenges in the daily lives of individuals, especially medical and governmental authorities as they are put under ...
A categorical study of persistent homology for closure space
(University of the Western Cape, 2023)
We begin with the concept of closure space and show how it relates to other objects like graphs and metric spaces in categorical terms. We also study the notion of simplicial sets and show that there is an adjunction between ...
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 ...