Masters Degrees (Statistics and Actuarial Science)

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    A Bayesian extreme value approach to the optimal reinsurance problem in a multivariate risk setting
    (Stellenbosch : Stellenbosch University, 2023-12) Steenkamp, Shaun Francois; Harvey, Justin; Stellenbosch University. Faculty of Economic and Management Sciences. Dept. of Statistics and Actuarial Science.
    ENGLISH SUMMARY: This thesis investigates a Bayesian extreme value theory approach to analyse the optimal reinsurance problem, more specifically the optimal layer selection of an excess of loss reinsurance contract. This thesis suggests a simulation approach to the optimization of the layer selection. This thesis proposes a multivariate excess of loss (XL) reinsurance structure, referred to as the simultaneous XL reinsurance structure and applies the developed optimization algorithm to this structure in several numerical examples. The approach takes a particular focus on extreme risks, thereby investigating the optimal reinsurance contract that best protects the insurance company from rare large claims. The methodology is explained for a univariate risk case, thereafter the model is extended to the bivariate and the multivariate risk cases. The optimal reinsurance agreement can be investigated using a variety of different models. This thesis develops a risk measure minimization model, with a focus on the conditional tail expectation (CTE) riskmeasure. The model allows for the insurance company’s reinsurance budget as a constraint in the optimization problem. Bayesian techniques are especially useful in problems where data is sparse, therefore this thesis suggests utilizing a Bayesian approach to the optimal reinsurance problem where rare large claims are considered. A Bayesian extreme value theory approach could improve the process of investigating the optimal reinsurance problem by utilising Markov Chain Monte Carlo (MCMC) methods to supplement the information from the data that the insurance company has available. The approach is extended into the bivariate and multivariate risk cases where a fictitious insurer, involved in various lines of business is considered. The dependence structure is modelled using a copula approach. Numerical examples are examined, and the results are interpreted. This thesis takes a focus on the tail of the data, thereby evaluating the optimal excess of loss reinsurance contract for very large claims with very small probabilities. The research suggests an algorithm for evaluating the optimal reinsurance strategy in a multivariate risk environment for insurance companies involved in different lines of business. The analysis will improve understanding and assist decision making on the reinsurance strategy from the insurer’s perspective.
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    Using valuation based on fundamental analysis to design an enhanced index based on the JSE Top 40 Index
    (Stellenbosch : Stellenbosch University, 2023-12) Gounder, Nathan David; Conradie, WJ; Stellenbosch University. Faculty of Economic and Management Sciences. Dept. of Statistics and Actuarial Science.
    ENGLISH SUMMARY: The idea of the index fund originated in the 1970s and while it was not popular back then, its popularity rose and today many investors have placed their trust in this investment product. The returns, mostly due to low fees, are the main attraction for investors to this product. Active managers have since tried to come up with ways to outperform these funds after fees with little success. Enhanced index funds were then designed to outperform their respective indices. The idea is to use active management methodologies applied to an index to outperform the index. This assignment designs an enhanced index based on intrinsic valuation to adjust the market weights of the JSE Top 40 to outperform the index while maintaining a low tracking error. Valuation is based mainly on cash flows but its adjustment depends on what industry the company is in. The weights are adjusted iteratively by 0.5%, 1% and 2%. Overvalued companies were underweighted while undervalued companies were over-weighted resulting in a net effect of 0. The results from this showed that before fees, the JSE Top 40 and the Satrix Top 40 fund were beaten at the 1% and 2% adjustment levels while after fees with reinvestment, the Enhanced index outperformed the JSE Top 40 index at all adjustment levels but only outperformed the Satrix Top 40 fund at the 2% adjustment level. After fees and without reinvestment, the Enhanced index outperformed the Satrix Top 40 fund at the 1% and 2%% adjustment levels but failed to outperform the JSE Top 40 at all levels.
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    Analysis to indicate the impact Hindsight Bias have on the outcome when forecasting of stock in the South African equity market
    (Stellenbosch : Stellenbosch University, 2023-12) Heyneke, Anton Lafrass; Conradie, Willie; Alfeus, Mesias; Stellenbosch University. Faculty of Economic and Management Sciences. Dept. of Statistics and Actuarial Science.
    ENGLISH SUMMARY: A novel Artificial Neural Network (ANN) framework presented in this study has the ability to mimic the effect that cognitive biases, specifically hindsight bias has on the financial market. This study investigates how hindsight bias influences models and their outcomes. During this study the hindsight bias effect will be measured within a South African context. The decisions that people make when faced with uncertainty are characterized by heuristic judgments and cognitive biases. If these characteristics are systematic and confirmed through research and literature related to this topic, it would form a quintessential part to the explanation of the behaviour of financial markets. This research presents a methodology that could be used to model the impact of cognitive biases on the financial markets. In this study, an ANN will be used as a stand-in for the decision-making process of an investor. It is important to note that the selection of the companies, on which the ANN will be trained, validated and tested, demonstrated cognitive bias during the study's preparation. Though there are many cognitive biases that have been identified in the literature on behavioural finance, this study will concentrate solely on the impact of hindsight bias. On financial markets, hindsight bias manifests when outcomes seem more predictable after they have already happened. This study attempts and succeeds – to some degree - to replicate the return characteristics of the ten chosen companies for the assessment period from 2010 to 2021. The study described here may still be subject to various cognitive biases and systemic behavioural errors in addition to the hindsight bias. The further application of this technique will stimulate further research with respect to the influence of investor behaviour on financial markets.
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    Enhancing realised volatility prediction in emerging markets
    (Stellenbosch : Stellenbosch University, 2023-12) Maphatsoe, Phuthehang; Alfeus, Mesias; Stellenbosch University. Faculty of Economic and Management Sciences. Dept. of Statistics and Actuarial Science.
    ENGLISH SUMMARY: This research assignment introduces a comprehensive framework aimed at improving the accuracy of realised volatility forecasts within the context of the South African financial market. The fundamental approach is rooted in the utilisation of high-frequency data and the employment of volatility models that effectively capture the inherent high persistence commonly observed in financial markets. The study is particularly centred on the evaluation of four distinct models: the Heterogeneous AutoRegressive (HAR), Generalised AutoRegressive Conditional Heteroscedasticity (realGARCH), R.ecurrent Conditional Heteroskedasticity (RECH), and the R.ough Fractional Stochastic Volatility (RFSV) models. Furthermore, the study extends these models to incorporate the South African implied volatility (IV), referred to as the South African Volatility Index (SAVI), as an exogenous variable, with the expectation that this augmentation will further refine the accuracy of volatility estimations. These selected models are intentionally designed to capture the intricate dynamics and long-range dependencies that are evident within financial time series, characteristics often overlooked by conventional forecasting methods. The empirical investigation is based on the examination of four key financial indices within the South African market. The findings of this extensive analysis highlight the distinctive performance of each model in terms of capturing long-term volatility patterns. Notably, the HAR model emerges as the most adept at capturing these enduring patterns, while the realGARCH, R.ECH, and RFSV models also display commendable performance, albeit to varying degrees. Furthermore, the inclusion of the SAVI as an exogenous variable is found to enhance the empirical fit and predictive capacity of the models. This enhancement is particularly evident when assessing forecasting accuracy across both one-day and multi-period horizons. These results affirm the effectiveness of the chosen models and provide valuable insights into their suitability for modelling the South African financial market's unique characteristics. In a broader context, this study offers essential insights into realised volatility forecasting within the South African financial market. The practical implications of these findings are substantial, as they provide practitioners and investors with the knowledge required to make well-informed decisions.
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    A study of fairness in machine learning in the presence of missing values
    (Stellenbosch : Stellenbosch University, 2023-03) Bhatti, Aeysha Aziz; Sandrock, Trudy; Stellenbosch University. Faculty of Economic and Management Sciences. Dept. of Statistics and Actuarial Science.
    ENGLISH SUMMARY: Fairness of Machine Learning algorithms is a topic that is receiving increasing attention, as more and more algorithms permeate the day to day aspects of our lives. One way in which bias can manifest in a data source is through missing values. If data are missing, these data are often assumed to be missing completely randomly, but usually this is not the case. In reality, the propensity of data being missing is often tied to socio-economic status or demographic characteristics of individuals. There is very limited research into how missing values and missing value handling methods can impact the fairness of an algorithm. In this research, we conduct a systematic study starting from the foundational questions of how the data are missing, how the missing data are dealt with and how this impacts fairness, based on the outcome of a few different types of machine learning algorithms. Most researchers, when dealing with missing data, either apply listwise deletion or tend to use the simpler methods of imputation versus the more complex ones. We study the impact of these simpler methods on the fairness of algorithms. Our results show that the missing data mechanism and missing data handling procedure can impact the fairness of an algorithm, and that under certain conditions the simpler imputation methods can sometimes be beneficial in decreasing discrimination.