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Theses and Dissertations (Mathematics and Applied Mathematics): Recent submissions

  • Zeros of irreducible characters of finite groups 
    Madanha, Sesuai Yasha (University of Pretoria, 2019)
    This work is a contribution to the classification of finite groups with an irreducible character that vanishes on exactly one conjugacy class. Specifically, in this thesis we study finite non-solvable groups G that satisfy ...
  • An ergodic theoretic approach to Szemerédi's theorem 
    Van Amstel, Sarel Jakobus van der Walt (University of Pretoria, 2018)
    In this dissertation, Szemer edi's Theorem is proven using ergodic theoretic techniques via the Furstenberg Multiple Recurrence Theorem. Brief historical remarks, along with a non-technical layout of the ideas behind the ...
  • A case study of arbitrage opportunities and efficiency of the JSE 
    Rapoeea, Nthabiseng Joyce (University of Pretoria, 2018)
    This dissertation examines the market efficiency and arbitrage opportunities between 04 January 2000 and 31 December 2015 on selected JSE-listed stocks and equity indices. To assess market efficiency, four tests were ...
  • The effect of conspecific support on the asymptotic properties of competing species 
    Phiri, Avulundiah Edwin (University of Pretoria, 2018)
    The long term properties, like coexistence and extinction, are usually determined by the demographics of the competing species or other competitive advantages. In this dissertation we consider the effect of conspecific ...
  • Mathematical models of the epidemiological dynamics of soil-borne pathogens 
    Bekker, Rebecca Anne (University of Pretoria, 2018)
    Despite the increase in agricultural crop yield over the last century, the world's food supply is in grave danger, as an estimated 16% of global yield is lost to various pathogens annually. As a result, mathematical ...
  • Valuing American Asian Options with Least Squares Monte Carlo and Low Discrepancy Sequences 
    Van Niekerk, Andries Jacobus (University of Pretoria, 2018)
    There exists no closed form approximation for arithmetically calculated Asian options, but research has shown that closed form approximations are possible for Geometrically calculated Asian options. The aim of this ...
  • Nonlinear Acoustics : what happens when the constraint is challenged? 
    Dziwa, Simbarashe Kudzai (University of Pretoria, 2017)
    The Lagrangian formulation for the propagation of sonic disturbances consists of a system of rst order partial di erential equations and an inequality constraint under which the system is hyperbolic. We study the behaviour ...
  • The use of risk measures and its applications in portfolio optimisation 
    Sivnarain, Resham (University of Pretoria, 2017)
    In this dissertation, we study the application of risk measures to portfolio optimisation. A risk measure is a functional over the set of random portfolio returns mappings . We present the various risk measures in this ...
  • Properties of a class of generalized Freud polynomials 
    Kelil, Abey (University of Pretoria, 2018)
    Semiclassical orthogonal polynomials are polynomials orthogonal with respect to semiclassical weights. The fascinating link between semiclassical orthogonal polynomials and discrete integrable equations can be traced back ...
  • Mathematical modelling and analysis of HIV/AIDS and trichomonas vaginalis co-infection 
    Mumba, Chibale K. (University of Pretoria, 2017)
    Deterministic models for the transmission dynamics of HIV/AIDS and trichomonas vaginalis (TV) in a human population are formulated and analysed. The models which assumed standard incidence formulations are shown to have ...
  • Stochastic optimal portfolios and life insurance problems in a Lévy market 
    Guambe, Calisto (University of Pretoria, 2018)
    This thesis solves various optimal investment, consumption and life insurance problems described by jump-diffusion processes. In the first part of the thesis, we solve an optimal investment, consumption, and life insurance ...
  • Portfolio risk measures and option pricing under a Hybrid Brownian motion model 
    Mbona, Innocent (University of Pretoria, 2017)
    The 2008/9 financial crisis intensified the search for realistic return models, that capture real market movements. The assumed underlying statistical distribution of financial returns plays a crucial role in the evaluation ...
  • A practical implementation of XVA in the new normal 
    Kairinos, Christopher (University of Pretoria, 2017)
    The Great Financial Crisis (GFC) of 2008 left many financial institutions devastated. Despite the practice of advanced risk management at the time, society witnessed the collapse of the “too big to fail” institutions. Gaping ...
  • Pricing Options under Levy models using Spectral methods 
    Youbi, Francis (University of Pretoria, 2017)
    Spectral methods have been actively developed in the last decades. The main advantage of these methods is to yield exponential order of accuracy when the function is smooth. However, for discontinuous functions, their ...
  • Existence results for a class of semi-linear initial value problems 
    Manicom, Gray Thomas (University of Pretoria, 2017)
    The main result of this thesis is an existence result for parabolic semi-linear problems. This is done by reformulating the semi-linear problem as an abstract Cauchy problem ut(t) = Au(t) + f(t; u(t)), t > 0 u(0) = u0 ...
  • Residuation in the set of topologizing filters of a ring 
    Chere, Nega Arega (University of Pretoria, 2016)
    Read abstract in the document
  • Numerical stabilization with boundary controls for hyperbolic systems of balance laws 
    Weldegiyorgis, Gediyon Yemane (University of Pretoria, 2016)
    In this dissertation, boundary stabilization of a linear hyperbolic system of balance laws is considered. Of particular interest is the numerical boundary stabilization of such systems. An analytical stability analysis ...
  • On the algebra of relevance logics 
    Wannenburg, Johann Joubert (University of Pretoria, 2016)
    After recalling some prerequisites from universal algebra in Chapter 1, we recount in Chapter 2 the general theory of deductive (logical) systems. As working examples, we consider the exponential-free fragment CLL of ...
  • Magnetohydrodynamic turbulent flows for viscous incompressible fluids through the lenses of harmonic analysis 
    Tegegn, Tesfalem Abate (University of Pretoria, 2016)
    This thesis is divided into three main parts devoted to the study of magnetohydrodynamics (MHD) turbulence flows. Part I consists of introduction and background (or preliminary) materials which were crucially important ...
  • A finite element approach to pricing Barrier options 
    Richards, Mark Timothy (University of Pretoria, 2015)
    In this dissertation we consider the valuation of discretely monitored barrier options under the in nite element method. The in nite element method is an extension to the standard nite element method that accepts ...