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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 ...
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. ...
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 ...
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 of the population dynamics of tuberculosis
(University of the Western Cape, 2016)
Tuberculosis (TB) is currently one of the major public health challenges in South Africa, and in many countries. Mycobacterium tuberculosis is among the leading causes of morbidity and mortality. It is known that tuberculosis ...
Mathematical modelling of HIV/AIDS with recruitment of infecteds
(University of the Western Cape, 2015)
The influx of infecteds into a population plays a critical role in HIV transmission. These infecteds are known to migrate from one region to another, thereby having some interaction with a host population. This interactive ...
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 ...
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 ...
A model of pension portfolios with salary and surplus process
(University of the Western Cape, 2010)
Essentially this project report is a discussion of mathematical modelling in pension funds, presenting sections from Cairns, A.J.D., Blake, D., Dowd, K., Stochastic lifestyling: Optimal dynamic asset allocation for defined ...