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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 ...
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 ...
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 ...
Stochastic modelling in bank management and optimization of bank asset allocation
(2009)
The Basel Committee published its proposals for a revised capital adequacy framework(the Basel II Capital Accord) in June 2006. One of the main objectives of this framework is to improve the incentives for state-of-the-art ...
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 ...
Discrete time methods of pricing Asian options
(University of Western Cape, 2014)
This dissertation studies the computation methods of pricing of Asian options. Asian options are options in which the underlying variable is the average price over a period of time. Because of this, Asian options have a ...
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 ...
Mathematical modelling of the HIV/AIDS epidemic and the effect of public health education
(University of Western Cape, 2014)
HIV/AIDS is nowadays considered as the greatest public health disaster of modern time.
Its progression has challenged the global population for decades. Through mathematical
modelling, researchers have studied different ...
Mathematical modeling of population dynamics of HIV with antiretroviral treatment and herbal medicine
(University of Western Cape, 2014)
Herbal medicines have been an important part of health and wellness for hundreds of
years. Recently the World Health Organization estimated that 80% of people worldwide
rely on herbal medicines. Herbs contain many ...