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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 ...
Fractional Black-Scholes equations and their robust numerical simulations
(University of Western Cape, 2020)
Conventional partial differential equations under the classical Black-Scholes approach
have been extensively explored over the past few decades in solving option
pricing problems. However, the underlying Efficient Market ...
Graphs of integral distance and their properties
(University of Western Cape, 2021)
Understanding the geometries of points in space has been attractive to mathematicians
for ages. As a model, twelve years ago, Kurz and Meyer [32] considered point
sets in the m-dimensional a ne space Fmq
over a nite ...
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 ...
Measurements of edge uncolourability in cubic graphs
(University of the Western Cape, 2020)
The history of the pursuit of uncolourable cubic graphs dates back more than a century.
This pursuit has evolved from the slow discovery of individual uncolourable
cubic graphs such as the famous Petersen graph and the ...
Efficient Variable Mesh Techniques to solve Interior Layer Problems
(University of Western Cape, 2020)
Singularly perturbed problems have been studied extensively over the past
few years from different perspectives. The recent research has focussed on the
problems whose solutions possess interior layers. These interior ...
Fractional black-scholes equations and their robust numerical simulations
(University of the Western Cape, 2020)
Conventional partial differential equations under the classical Black-Scholes approach
have been extensively explored over the past few decades in solving option
pricing problems. However, the underlying Efficient Market ...
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, ...
Mathematical modeling of TB disease dynamics in a crowded population.
(University of the Western Cape, 2020)
Tuberculosis is a bacterial infection which is a major cause of death worldwide. TB is a
curable disease, however the bacterium can become resistant to the first line treatment
against the disease. This leads to a disease ...
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 ...