Browsing by Author "Okoye-Ogbalu, Izuchukwu."

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Exploring pre-service mathematics teachers’ knowledge of logarithm in one of the universities in Kwazulu-Natal.
(2019) Okoye-Ogbalu, Izuchukwu.; Mthethwa, Themba Mngomeni.
The use of logarithm, an important tool for calculus and beyond, has been reduced to symbol manipulation without understanding in most entry-level college algebra courses. In most secondary school mathematics curriculum, particularly in South Africa, logarithm just occurs as the inverse function of an exponential function without a detailed explanation of the logarithm itself. The primary aim of this research, therefore, was to explore pre-service mathematics teachers’ knowledge of logarithm through the use of a research task designed to observe what pre-service mathematics teachers know as they solve the problems and through the use of interview to understand how they solve the problems. Constructivism theory was used as a framework for the analysis and the interpretation of how pre-service teachers conceptualize logarithm. Constructivism theory is a useful theoretical framework for studying and explaining conceptual development through prior knowledge. This is a qualitative study conducted in one of the universities in the province of KwaZulu-Natal. The findings of this study reveal that most pre-service mathematics teachers do not have a good knowledge of logarithm. This is why they have difficulties in solving problems involving logarithm. The findings also reveal that pre-service mathematics teachers do not have good knowledge of logarithm because of how the concept of logarithm was introduced to them in secondary school. The study concludes by recommending that lecturers in the mathematics discipline should try to design teaching material that targets the development of conceptual understanding and pre-service mathematics teachers need to develop sufficient sense of dealing with more abstract concepts in order to do justice in the teaching of logarithm at the secondary school level.
Pricing and hedging of defaultable claims in discontinuous market.
(2017) Okoye-Ogbalu, Izuchukwu.; Tchoukouegno Ngnotchouye, Jean Medard.; Pamen, Olivier Menoukeu.
Credit risk has become one of the highest-pro le risk facing participants in the nancial markets. In this dissertation, we study the pricing and hedging of defaultable claim in a discontinuous market. Here, we present the pricing of credit default swap under stochastic intensity within the set up of a generic reduced form credit risk model. In this context, we present di erent approaches to pricing and hedging of defaultable claim in a discontinuous market and then pro er results concerning the trading of credit default swap. We rst assume that the default intensity is deterministic and the rate of interest is equal to zero. We derive a closed-form solution for replicating strategy for an arbitrary non-dividend paying defaultable claim. We then extend the established results under deterministic intensity to the case of stochastic intensity, where the objective is to hedge both default (jump) risk and the spread (volatility) risk.