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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 ...
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 ...
Mathematical models of credit management and credit derivatives
(2010)
The first two chapters give the background, history and overview of the dissertation, together with the necessary mathematical preliminaries. Thereafter, the next four chapters deal with credit risk and credit derivatives.The ...
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 ...
A mathematical modeling of optimal vaccination strategies in epidemiology
(University of the Western Cape, 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 ...
Strong simplicity of groups and vertex - transitive graphs
(University of the Western Cape, 2010)
In the course of exploring various symmetries of vertex-transitive graphs, we introduce the concept of quasi-normal subgroups in groups. This is done since the symmetries of vertex-transitive graphs are intimately linked ...
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 ...
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 ...
The influence of interfaces on the understanding of Mathematics in secondary schools in Afghanistan
(University of the Western Cape, 2010)
The focus of this research is to establish whether there is a difference in the way the genders perceive the visualization of mathematics, with specific reference to set theory. The influence of the computing experience ...
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 ...