Hybrid pension plans offer employees the best features of both defined benefit and defined contribution plans. In this work, we consider the hybrid design offering a defined contribution benefit with a defined benefit guaranteed minimum underpin. This study applies the contingent claims approach to value the defined contribution benefit with a defined benefit guaranteed minimum underpin. The study shows that entry age, utility function parameters and the market price of risk each has a significant effect on the value of retirement benefits. We also consider risk management for this defined benefit underpin pension plan. Assuming fixed interest rates, and assuming that salaries can be treated as a tradable asset, contribution rates are developed for the Entry Age Normal (EAN), Projected Unit Credit(PUC), and Traditional Unit Credit (TUC) funding methods. For the EAN, the contribution rates are constant throughout the service period. However, the hedge parameters for this method are not tradable. For the accruals method, the individual contribution rates are not constant. For both the PUC and TUC, a delta hedge strategy is derived and explained. The analysis is extended to relax the tradable assumption for salaries, using the inflation as a partial hedge. Finally, methods for incorporating volatility reducingand risk management are considered.

In the context of the guarantee liability valuation, the sophisticated fund-of-funds structure, of some Canadian segregated fund products, often requires us to model multiple market indices simultaneously in order to benchmark the return of the underlying fund. In this thesis, we apply multivariate GARCH models with Gaussian and non-Gaussian noise to project the future investment scenarios of the fund. We further conduct a simulation study to investigate the difference, among the proposed multivariate models, in the valuation of the Guaranteed Minimum Maturity Benefit (GMMB) option. Based on the pre-data analysis, the proposed multivariate GARCH models are data driven. The goodness-of-fit for the models is evaluated through formal statistical tests from univariate and multivariate perspectives. The estimation and associated practical issues are discussed in details. The impact from the innovation distributions is addressed. More importantly, we demonstrate an actuarial approach to manage the guarantee liability for complex segregated fund products.

In this thesis, an attempt is made to build on the quantitative research in the field of Islamic Finance. Firstly, univariate modelling using special GARCH-type models is performed on both the FTSE All World and FTSE Shari'ah All World indices. The AR(1) + APARCH(1,1) model with standardized skewed student-t innovations provided the best overall fit and was the most successful at VaR modelling for long and short trading positions. A risk assessment is done using the Conditional Tail Expectation (CTE) risk measure which concluded that in short trading positions the FTSE Shari'ah All World index was riskier than the FTSE All World index but, in long trading positions the results were not conclusive as to which is riskier. Secondly, under the Markowitz model of risk and return the performance of Islamic equity is compared to conventional equity using various Dow Jones indices. The results indicated that even though the Islamic portfolio is relatively less diversified than the conventional portfolio, due to several investment restrictions, the Shari'ah screening process excluded various industries whose absence resulted in risk reduction. As a result, the Islamic portfolio provided a basket of stocks with special and favourable risk characteristics. Lastly, copulas are used to model the dependency structure between the filtered returns of the FTSE All World and FTSE Shari'ah All World indices after fitting the AR(1) + APARCH(1,1) model with standardized skewed student-t innovations. The t copula outperformed the others and a demonstration of forecasting using the copula-extended model is done.

Infant and child mortality rates are one of the health indicators in a given community or country. It is the fourth millennium development goal that by 2015, all the united nations member countries are expected to have reduced their infant and child mortality rates by two-thirds. Uganda is one of those countries in sub-Saharan Africa with high infant and child mortality rates and therefore has the need to find out the factors strongly associated to these high rates in order to provide alternative or maintain the existing interventions. The Uganda Demographic Health Survey (UDHS) funded by USAID, UNFPA, UNICEF, Irish Aid and the United kingdom government provides a data set which is rich in information. This information has attracted many researchers and some of it can be used to help Uganda monitor her infant and child mortality rates to achieve the fourth millennium goal. Survival analysis techniques and frailty modelling is a well developed statistical tool in analysing time to event data. These methods were adopted in this thesis to examine factors affecting under-five child mortality in Uganda using the UDHS data for 2011 using R and STATA software. Results obtained by fitting the Cox-proportional hazard model and frailty models and drawing inference using both the Frequentists and Bayesian approach showed that, Demographic factors (sex of the household head, sex of the child and number of births in the past one year) are strongly associated with high under-five child mortality rates. Heterogeneity or unobserved covariates were found to be signifcant at household but insignifcant at community level. / Thesis (M.Sc.)-University of KwaZulu-Natal, Pietermaritzburg, 2013.

Survival analysis is a well developed area which explores time to single event analysis. In some cases, however, such methods may not adequately capture the disease process as the disease progression may involve intermediate events of interest. Multistate models incorporate multiple events or states. This thesis proposes to demystify the theory of multistate models through an application based approach. We present the key components of multistate models, relevant derivations, model diagnostics and techniques for modeling the effect of covariates on transition intensities. The methods that are developed in the thesis are applied to HIV and TB data partly sourced from CAPRISA and the HPP programmes in the University of KwaZulu-Natal. HIV progression is investigated through the application of a five state Markov model with reversible transitions such that state 1: CD4 count 500, state 2: 350 CD4 count < 500, state 3: 200 CD4 count < 350, state 4: CD4 count < 200 and state 5: ARV initiation. The mean sojourn time in each state and transition probabilities are presented as well as the effect of covariates namely age, gender and baseline CD4 count on transition rates. A key finding, consistent with previous research, is that the rate of decline in CD4 count tends to decrease at lower levels of the marker. Further, patients enrolling with a CD4 count less than 350 had a far lower chance of immune recovery and a substantially higher chance of immune deterioration compared to patients with a higher CD4 count. We noted that older patients tend to progress more rapidly through the disease than younger patients. / Thesis (M.Sc.)-University of KwaZulu-Natal, Westville, 2011.

No abstract available. / Thesis (M.Sc.)-University of Durban-Westville, 1992.

The option pricing theory set forth by Black and Scholes assumes that the underlying asset can be modeled by Geometric Brownian motion, with the Brownian motion being the driving force of uncertainty. Recent empirical studies, Dotsis, Psychoyios & Skiadopolous (2007) [17], suggest that the use of Brownian motion alone is insufficient in accurately describing the evolution of the underlying asset. A more realistic description of the underlying asset’s dynamics would be to include random jumps in addition to that of the Brownian motion. The concept of including jumps in the asset price model leads us naturally to the concept of a L'evy process. L'evy processes serve as a building block for stochastic processes that include jumps in addition to Brownian motion. In this dissertation we first examine the structure and nature of an arbitrary L'evy process. We then introduce the stochastic integral for L'evy processes as well as the extended version of Itˆo’s lemma, we then identify exponential L'evy processes that can serve as Radon-Nikod'ym derivatives in defining new probability measures. Equipped with our knowledge of L'evy processes we then implement this process in a financial context with the L'evy process serving as driving source of uncertainty in some stock price model. In particular we look at jump-diffusion models such as Merton’s(1976) [37] jump-diffusion model and the jump-diffusion model proposed by Kou and Wang (2004) [30]. As the L'evy processes we consider have more than one source of randomness we are faced with the difficulty of pricing options in an incomplete market. The options that we shall consider shall be mainly European in nature, where exercise can only occur at maturity. In addition to the vanilla calls and puts we independently derive a closed form solution for an exchange option under Merton’s jump-diffusion model making use of conditioning arguments and stochastic integral representations. We also examine some exotic options under the Kou and Wang model such as barrier options and lookback options where the solution to the option price is derived in terms of Laplace transforms. We then develop the Kou and Wang model to include only positive jumps, under this revised model we compute the value of a perpetual put option along with the optimal exercise point. Keywords Derivative pricing, L'evy processes, exchange options, stochastic integration. / Thesis (M.Sc.)-University of KwaZulu-Natal, Westville, 2009.

This thesis explores option pricing and hedging in a discrete time regime-switching environment. If the regime risk cannot be hedged away, then we cannot ignore this risk and use the Black-Scholes pricing and hedging framework to generate a unique pricing and hedging measure. We develop a risk neutral pricing measure by applying an Esscher Transform to the real world asset price process, with the focus on the issue of incompleteness of the market. The Esscher transform turns out to be a convenient and effective tool for option pricing under the discrete time regime switching models. We apply the pricing measure to both single variate European options and multivariate options. To better understand the effect of the pricing method, we also compared the results with those generated from two other risk neutral methods: the Black-Scholes model, and the natural equivalent martingale method. We further investigate the difference in hedging associated with different pricing measures. This is of interest when the choice of pricing method is uncertain under regime switching models. We compare four hedging strategies: delta hedging for the three risk neutral pricing methods under study, and mean variance hedging. We also develop a more general tool of tail ordering for hedging analysis in a general incomplete market with the uncertainty of the risk neutral measures. As a result of the analysis, we propose that pricing and hedging using the Esscher transform may be an effective strategy for a market where the regime switching process brings uncertainty.

The interplay between remarriage and fertility is among the most poorly documented subjects in sub-Saharan Africa, yet remarriage is one of the fundamental aspects of marriage dynamics in the region. Referring to classical demographic and statistical techniques, this research uses data collected since 1992 from Malawi Demographic and Health Surveys to establish the pattern and level of union dissolution and remarriage, and to assess the influence of remarriage on fertility preference and childbearing. The results reveal increasing stability of unions over time and a declining proportion of remarried women. The probability of experiencing first union dissolution within 15 years dropped from 45.9 to 40.0 per cent between 1992 and 2015, while the comparable likelihood of remarriage decreased from 36.1 to 27.7 per cent over the same interval duration. The effect of remarriage on the desire for more children is positive at advanced interval durations relative to the onset of first marriage. At shorter interval periods, where remarriage is relatively most recent, remarriage inhibits the desire for additional children. For example, in 2015, among women who first married 15-19 years before the survey, the odds of desiring another child were 4 per cent significantly higher among remarried women relative to their counterparts in intact unions. In contrast, for women who were married for 0-5 years, remarried women had 3 per cent lower olds of desiring another child. Furthermore, the childbearing pattern of remarried women is found to be distinct from that of women in intact unions. Remarried women give birth to more children sooner than their counterparts in intact unions, but eventually end up with fewer children. Indeed, the results show that in 2015, women in intact unions had 0.4 more children on average than their remarried counterparts. However, the difference in complete family size is steadily diminishing (difference of 1.5 in 2000), largely due to more marked fertility decline among women in intact unions. This trend, together with the long-term pattern of cumulated fertility differentials at younger reproductive ages, and current fertility disparities over the past two decades, strongly reveals that a new regime, where remarried women will end up with higher complete family size than those in intact unions, is emerging.

Actuarial Science is a sought after profession in South Africa with high attrition rates at university. The profession is small and dominated by white males. Slow transformation of the profession to reflect a more representative sample of the population is exacerbated by the long route to qualification. This study is an analysis of the first module of the redesigned course reader for the course 'Introduction to Actuarial Science' at the University Cape Town. It was prompted by the change in student engagement with and sentiment about the course in 2013. Data is concurrently analysed from two interviews with the course convenor exploring (a) the nature and description of the profession as well as what knowledge is valued in the field of practice and the discipline and (b) the reasons for the redesign of the course reader and the process itself. The first module of the course reader is analysed in tandem with the second interview data. The research aims to reveal the complexity of the knowledge of actuarial science which makes mastery of its content, methods and ways of thinking (summed up in the term epistemic access ) challenging. Thus careful curriculum design is important in orientating first year students to the discipline and profession. Educational theorists from the school of social realism provide conceptual frameworks through which one can identify knowledge structures and elements thereof in data. Basil Bernstein's Pedagogic Device is used in locating the course reader data in the field of recontextualisation, relying on recontextualising rules which 'regulate the formation of specific pedagogic discourse' (Bernstein, 2000, p.28) to examine the ways in which access to the discipline is facilitated in the course reader. In addition, Bernstein's pedagogic codes analysed by means of his concepts classification and framing are employed to analyse (a) the nature and description of the profession and (b) the knowledge valued in the discipline and in the field of practice. Karl Maton's Legitimation Code Theory and in particular the identification of specialisation codes on the basis of epistemic and social relation s affords the potential of understanding the key principles by which this knowledge form is legitimated. The writings of Young (2008) and Muller (2009 and Young and Muller (201 4 ) assist in delineating a few crucial issues on professional knowledge and the curriculum. This project seeks to analyse the curriculum knowledge and the pedagogic codes employed in the course reader of a newly designed introductory course to ascertain the nature of actuarial science and to suggest what forms of pedagogy might enable students to access that knowledge. Regarding the nature of actuarial science, the study found that it is a complex region that combines highly specialized techno-theoretical knowledge with specific forms of inferential reasoning and professional judgment required to address knotty problems in the business world. Regarding an effective pedagogy, the analysis of the course reader provides clues as to what an explicit, visible pedagogic discourse capable of providing access to this complex field to first generation students might entail.