ENGLISH ABSTRACT: In this thesis, we propose to use Levy processes to model the dynamics of asset prices. Inthe first part, we deal with single asset options and model the log stock prices with a Levyprocess. We employ pure jump Levy processes of infinite activity, in particular variancegamma...

ENGLISH ABSTRACT: This research report investigated whether evidence of volatility clustering exists on the FTSE/JSE Top 40 Index. The presence of volatility clustering has practical implications relating to market decisions as well as the accurate measurement and reliable forecasting of...

This study aims to investigate whether the phenomena found by Shnoll et al. when applying histogrampattern analysis techniques to stochastic processes from chemistry and physics are also present infinancial time series, particularly exchange rate and index data. The phenomena are related to...

An overview of modern and historical interest rate model theory is given with thespecific aim of derivative pricing. A variety of stochastic interest rate models arediscussed within a South African market context. The various models arecompared with respect to characteristics such as mean...

We consider the problem of model assessment by risk estimation. Variousapproaches to risk estimation are considered in a uni ed framework. This a discussion of various complexity dimensions and approaches to obtainingbounds on covering numbers is also presented.The second type of training sample...

This paper discusses the relationship between two threads of social science research: traditional analysis of healthcare market failures and criticism of the narrow assumptions economic models make. The results that the American healthcare system produces are relatively poor compared to other...

In this dissertation we present mathematical models that help answer health policy questions relating to HIV and Hepatitis C (HCV), and analyze bias in Markov models of disease progression. We begin by developing a Markov decision process model that examines the timing of testing and treatment...

Due to increasing interest in sustainable development, today s engineer is often tasked with designing systems that are environmentally benign over their entire life cycles. Unfortunately, environmental assessments commonly suffer from significant uncertainty due to lack of information,...

The use of computer modeling is fast increasing in almost everyscientific, engineering and business arena. This dissertationinvestigates some challenging issues in design, modeling andanalysis of computer experiments, which will consist of four majorparts. In the first part, a new approach is...

Research in this thesis deals with some unexplored, or only partially explored, issues relating to the information content of volatility of the idiosyncratic component of asset returns at the firm and industry-level, both in the context of developed and emerging stock markets. Specific issues we...