Peak electricity demand is an energy policy concern for all countries throughout the world, causing blackouts and increasing electricity tariffs for consumers. This calls for load curtailment strategies to either redistribute or reduce electricity demand during peak periods. This thesis attempts to address this problem by providing relevant information through a frequentist and Bayesian modelling framework for daily peak electricity demand using South African data. The thesis is divided into two parts. The first part deals with modelling of short term daily peak electricity demand. This is done through the investigation of important drivers of electricity demand using (i) piecewise linear regression models, (ii) a multivariate adaptive regression splines (MARS) modelling approach, (iii) a regression with seasonal autoregressive integrated moving average (Reg-SARIMA) model (iv) a Reg-SARIMA model with generalized autoregressive conditional heteroskedastic errors (Reg-SARIMA-GARCH). The second part of the thesis explores the use of extreme value theory in modelling winter peaks, extreme daily positive changes in hourly peak electricity demand and same day of the week increases in peak electricity demand. This is done through fitting the generalized Pareto, generalized single Pareto and the generalized extreme value distributions. One of the major contributions of this thesis is quantification of the amount of electricity which should be shifted to off peak hours. This is achieved through accurate assessment of the level and frequency of future extreme load forecasts. This modelling approach provides a policy framework for load curtailment and determination of the number of critical peak days for power utility companies. This has not been done for electricity demand in the context of South Africa to the best of our knowledge. The thesis further extends the autoregressive moving average-exponential generalized autoregressive conditional heteroskedasticity model to an autoregressive moving average exponential generalized autoregressive conditional heteroskedasticity-generalized single Pareto distribution. The benefit of this hybrid model is in risk modelling of under and over demand predictions of peak electricity demand. Some of the key findings of this thesis are (i) peak electricity demand is influenced by the tails of probability distributions as well as by means or averages, (ii) electricity demand in South Africa rises significantly for average temperature values below 180C and rises slightly for average temperature values above 220C and (iii) modelling under and over demand electricity forecasts provides a basis for risk assessment and quantification of such risk associated with forecasting uncertainty including demand variability.

South African medical schemes spend billions of Rands each year on medical care costs for their beneficiaries near their end of life. Hospi-centric benefit design, fee-for-service reimbursement arrangements and fragmented, silo-based delivery of care result in high, often unnecessary spending near the end of life. Factors including an ageing population, increasing incidence rates of cancer and other non-communicable diseases, and high levels of multi-morbidity among beneficiaries near their end of life further drive end-of-life care costs. Low levels of hospice or palliative care utilisation, a high proportion of deaths in-hospital and chemotherapy use in the last weeks of life point to potentially poor-quality care near the end of life. The usual care pathway for serious illness near the end of life acts like a funnel into private hospitals. This often entails resource intensive care that includes aggressive care interventions right up until death. The result is potentially sub-optimal care and poor healthcare outcomes for many scheme beneficiaries and their surviving relatives. Understanding the complex nature of the end of life, the different care pathways, the available insurance benefits, the interactions between key stakeholders and the multitude of factors that drive end-of-life care costs are vital to setting end-of-life care reform in motion. In order to increase value at the end of life, i.e. to increase quality and/or to reduce costs, benefit design reform, alternative reimbursement strategies, effective communication and multi-stakeholder buy-in is key.

Post the Millennium Development Goal project a significant number of countries are still faced with the challenge of monitoring child mortality. Despite numerous enquiries since 1996 to provide this basic health indicator, South Africa has experienced prolonged periods of uncertainty regarding the level and trend of infant and under-5 mortality. The thesis develops an analytical framework to review all available data sources and methods of analysis and presents the results of the four approaches adopted to measure child mortality trends. Reviewing the demographic indicators produced from seven census and survey enquiries, the overall performance and the strengths and limitations of each approach is evaluated. Poor and extremely poor quality of data for child mortality emerges as a pervasive challenge to census and survey data. The thesis presents the remarkable improvement in the completeness of birth and death registration through South Africa's CRVS system, particularly since 2000, illustrating the possibility of using CRVS data to monitor provincial child mortality in the future and highlighting statistical challenges arising from the movement of children. In conclusion, South Africa should focus on improving CRVS for purposes of monitoring childhood mortality provincially and the comprehensive evaluation of available data is a useful lesson for other upper-middle-income countries.

Banks are key to a well-functioning economy. Periods of economic stress could put banks and therefore the financial system at risk so regulators such as the Prudential Authority in South Africa need to know if banks are resilient to economic stress. A model that forecasts the impact of severe economic stress is developed using publicly available information. The model forecasts the credit losses, deposit volumes and other general equity movements of the biggest five full-service South African banks to assess capital and liquidity strain for any defined macroeconomic stress scenario over the next 3 years. The full-service banks being considered account for more than 90% of all bank lending in deposits in the market and therefore covers the vast majority of banking systemic risk in South Africa. It is shown that different macroeconomic factors affect these banks in different ways due to differences in the type of customers with deposits with each institution and differences in credit risk associated with various loan products. From an overall market perspective economic growth, lending levels, household debt levels and equity markets are the key drivers of deposit volumes. Credit risk in turn is primarily driven by interest rates, inflation and household debt to disposable income. / Dissertation (MSc (Actuarial Science))--University of Pretoria, 2020. / Insurance and Actuarial Science / MSc (Actuarial Science) / Unrestricted

In developing countries, vital registration is the best source of death data that can be used to estimate adult mortality provided they are sufficiently complete. However, they are usually insufficient for estimating mortality sub-nationally due to incomplete registration. This research adapts a method used by Dorrington, Moultrie and Timæus at the provincial level to determine whether it is adequate for estimating adult mortality at the district municipality level in the year prior to the 2001 census. The method uses registration data adjusted for completeness of registration to scale (up or down) the deaths reported by households in the census by age group for each sex. The process of correcting the registered deaths in the year prior to the 2001 census involves estimating intercensal completeness for each population group and each sex between 1996 and 2001 using the average of results from the GGB and the SEG+δ methods. Thereafter, the results are used to estimate the completeness in each of the years within the intercensal period. Thus, an estimate of completeness is obtained in the year prior to the 2001 census for correcting the registered deaths at the population group level. These registered deaths are then used to obtain population group specific adjustment factors to correct the deaths reported by households at the district level, and thereafter to estimate adult mortality rates. Most districts in Kwa-Zulu-Natal have amongst the highest rates of adult mortality, while most districts in the Western Cape have amongst the lowest rates. Results show the Buffalo metropolitan municipality to have higher mortality than that expected for most of the district metropolitan municipalities for both sexes. The same is true for women in Mangaung metropolitan district. It is suspected that HIV prevalence had a significant impact on different levels of adult mortality in the districts, although some adults in the more urban provinces may have died in other provinces. At the provincial level, the method produces marginally higher estimates of adult mortality than the other sources. Provinces that reflect a higher level of mortality appear to deviate more from other research findings than those reflecting lower mortality. In conclusion, the method produces district estimates of ₄₅q₁₅ that are consistent with provincial estimates from other sources and with estimates of HIV prevalence at the district level.

Includes bibliographical references / Over the last few decades, there has been vast interest in the modelling of asset returns using jump diffusion processes. This was in part as a result of the realisation that the standard diffusion processes, which do not allow for jumps, were not able to capture the stylized facts that return distributions are leptokurtic and have heavy tails. Although jump diffusion models have been identified as being useful to capture these stylized facts, there has not been consensus as to how these jump diffusion models should be calibrated. This dissertation tackles this calibration issue by considering the basic jump diffusion model of Merton (197G) applied to South African equity and interest rate market data. As there is little access to frequently updated volatility surfaces and option price data in South Africa, the calibration methods that are used in this dissertation are those that require historical returns data only. The methods used are the standard Maximum Likelihood Estimation (MLE) approach, the likelihood profiling method of Honore (1998), the Method of Moments Estimation (MME) technique and the Expectation Maximisation (EM) algorithm. The calibration methods are applied to both simulated and empirical returns data. The simulation and empirical studies show that the standard MLE approach sometimes produces estimators which are not reliable as they are biased and have wide confidence intervals. This is because the likelihood function required for the implementation of the MLE method is not bounded. In the simulation studies, the MME approach produces results which do not make statistical sense, such as negative variances, and is thus not used in the empirical analysis. The best method for calibrating the jump diffusion model to the empirical data is chosen by comparing the width of the bootstrap confidence intervals of the estimators produced by the methods. The empirical analysis indicates that the best method for calibrating equity returns is the EM approach and the best method for calibrating interest rate returns is the likelihood profiling method of Honore (1998).

Arbitrageurs play an important role in keeping market prices close to their fundamental values by providing market liquidity. Most arbitrageurs however use leverage. When funding conditions worsen they are forced to reduce their positions. The resulting selling pressure depresses market prices, and in certain situations, pushes arbitrage spreads to levels exceeding many standard deviations. This phenomenon drove many century old financial institutions into bankruptcy during the 2007−2009 financial crisis. In this thesis, we provide empirical evidence and demonstrate analytically the effects of funding liquidity on arbitrage. We further discuss the implications for risk management. To conduct our empirical studies, we construct a novel Funding Liquidity Stress Index (FLSI) using principal components analysis. Its constituents are measures representing various funding channels. We study the relationship between the FLSI index and three di↵erent arbitrage strategies that we reproduce with real and daily transactional data. We show that the FLSI index has a strong explanatory power for changes in arbitrage spreads, and is an important source of contagion between various arbitrage strategies. In addition, we perform “event studies” surrounding events of changing margin requirements on futures contracts. The “event studies” provide empirical evidence supporting important assumptions and predictions of various theoretical work on market micro-structure. Next, we explain the mechanism through which funding liquidity affects arbitrage spreads. To do so, we study the liquidity risk premium in a market micro-structure framework where market prices are determined by the supply and demand of securities. We extend the model developed by Brunnermeier and Pedersen [BP09] to multiple periods and generalize their work by considering all market participants to be risk-averse. We further decompose the liquidity risk premium into two components: 1) a fundamental risk premium and 2) a systemic risk premium. The fundamental risk premium compensates market participants for providing liquidity in a security whose fundamental value is volatile, while the systemic risk premium compensates them for taking positions in a market that is vulnerable to funding liquidity. The first component is therefore related to the nature of the security while the second component is related to the fragility of the market micro-structure (such as leverage of market participants and margin setting mechanisms).

Arbitrageurs play an important role in keeping market prices close to their fundamental values by providing market liquidity. Most arbitrageurs however use leverage. When funding conditions worsen they are forced to reduce their positions. The resulting selling pressure depresses market prices, and in certain situations, pushes arbitrage spreads to levels exceeding many standard deviations. This phenomenon drove many century old financial institutions into bankruptcy during the 2007−2009 financial crisis. In this thesis, we provide empirical evidence and demonstrate analytically the effects of funding liquidity on arbitrage. We further discuss the implications for risk management. To conduct our empirical studies, we construct a novel Funding Liquidity Stress Index (FLSI) using principal components analysis. Its constituents are measures representing various funding channels. We study the relationship between the FLSI index and three di↵erent arbitrage strategies that we reproduce with real and daily transactional data. We show that the FLSI index has a strong explanatory power for changes in arbitrage spreads, and is an important source of contagion between various arbitrage strategies. In addition, we perform “event studies” surrounding events of changing margin requirements on futures contracts. The “event studies” provide empirical evidence supporting important assumptions and predictions of various theoretical work on market micro-structure. Next, we explain the mechanism through which funding liquidity affects arbitrage spreads. To do so, we study the liquidity risk premium in a market micro-structure framework where market prices are determined by the supply and demand of securities. We extend the model developed by Brunnermeier and Pedersen [BP09] to multiple periods and generalize their work by considering all market participants to be risk-averse. We further decompose the liquidity risk premium into two components: 1) a fundamental risk premium and 2) a systemic risk premium. The fundamental risk premium compensates market participants for providing liquidity in a security whose fundamental value is volatile, while the systemic risk premium compensates them for taking positions in a market that is vulnerable to funding liquidity. The first component is therefore related to the nature of the security while the second component is related to the fragility of the market micro-structure (such as leverage of market participants and margin setting mechanisms).

Child mortality can be used to measure the level of social development as well as the health status of children (Hill 1991). By world regions, sub-Saharan Africa maintains the highest rates of under-five mortality. Current under-five mortality is estimated at 76 deaths per 1,000 live births (Hug, Sharrow, Zhong et al. 2018). In Zambia, under-five mortality reached a peak of 197 in 1996 and is currently estimated at 60 (Hug, Sharrow, Zhong et al. 2018). On the world health agenda, reducing child mortality has been made a priority, especially for low income countries that remain the most affected. Among the targets of the Sustainable Development Goals (SDGs) is reduction of neonatal mortality to at least 12 deaths per 1,000 live births and under-five mortality to 25 deaths by 2030 (United Nations 2015). HIV/AIDS is one of the leading causes of mortality in Zambia and has contributed to the slow decline of under-five mortality (Garenne and Gakusi 2006). Children under the age of five years get infected with HIV mainly through vertical transmission (Fishel, Ren, Barrère et al. 2014). In the absence of treatment, vertical transmission of HIV is high and can range between 15 and 45 per cent, reducing below 5 per cent with effective interventions (Barral, Oliveira, Lobato et al. 2014). Despite vertical transmission being the main pathway through which children get infected with HIV, little research has been done to determine the significance of maternal HIV status on under-five mortality in Zambia. The aim of the study was, therefore, to determine the extent to which mortality of children with HIV-positive mothers differs from that of children with HIV-negative mothers. The Zambia Demographic and Health Survey (ZDHS) data for 2007 and 2014 which contain HIV serotesting data were used. Survival analysis using Poisson regression was used to model the influence of maternal HIV status taking into account confounding factors. The results of the study indicate that maternal HIV status was significantly associated with child mortality in both survey periods but by 2013/14 the influence of maternal HIV status had reduced and was insignificant for children born within one year of the 2013/14 survey. The reduction in the risk of dying between the inter-survey period may be as a result of increased coverage of prevention of mother-to-child transmission (PMTCT) and antiretroviral therapy (ART) services over the years. In order to reach universal coverage, there is need for increased provision of PMTCT and ART treatments and support for HIV strategies such as the 90 90 90 target.

Thesis (MComm (Statistics and Actuarial Science))--University of Stellenbosch, 2005. / Extremes are unusual or rare events. However, when such events – for example earthquakes, tidal waves and market crashes - do take place, they typically cause enormous losses, both in terms of human lives and monetary value. For this reason, it is of critical importance to accurately model extremal events. Extreme value theory entails the development of statistical models and techniques in order to describe and model such rare observations. In this document we discuss aspects of extreme value theory. This theory consists of two approaches: The classical maxima method, based on the properties of the maximum of a sample and the more popular threshold theory, based upon the properties of exceedances of a specified threshold value. This document provides the practitioner with the theoretical and practical tools for both these approaches. This will enable him/her to perform extreme value analyses with confidence. Extreme value theory – for both approaches - is based upon asymptotic arguments. For finite samples, the limiting result for the sample maximum holds approximately only. Similarly, for finite choices of the threshold, the limiting distribution for exceedances of that threshold holds only approximately. In this document we investigate the quality of extreme value based inferences with regard to the unknown underlying distribution when the sample size or threshold is finite. Estimation of extreme tail quantiles of the underlying distribution, as well as the calculation of confidence intervals, are typically the most important objectives of an extreme analysis. For that reason, we evaluate the accuracy of extreme based inferences in terms of these estimates. This investigation was carried out using a simulation study, performed with the software package S-Plus.