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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    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.
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    Economic capital allocation to market and survival risk for pure endowment products
    (Stellenbosch : Stellenbosch University, 2023-03) Pretorius, Jaco Harm; Louw, Simon; Stellenbosch University. Faculty of Economic and Management Sciences. Dept. of Statistics and Actuarial Science.
    ENGLISH ABSTRACT: Economic capital allocation to interest and longevity rate risks is a topic of interest for life insurers. This study aims to provide approaches to allocate the overall economic capital amount into market and survival risk components for a pure endowment product. The calculation of the economic capital figure can be done using either analytical or simulation-based methods. An allocation approach found in literature is then applied to the simulation-based capital quantification. An allocation approach for the analytical method is proposed. A pure endowment contract which faces risks that have been calibrated to a regulatory shock environment over one year backed by a six-month fixed interest risk free asset was used as case study for these allocation approaches. Both methods deliver comparable results, and both conclude that interest rate risk is much more important than the longevity component. The importance of interest rate risks depending on method range between 97% and 99.97% of economic capital allocated to this risk. Sensitivity analysis proved particularly insightful in this study. We found that the analytical approach is more sensitive to the methodology choice in the decomposition step. Both methods provide sensible behaviour across different parameter values. The main advantage of the simulation-based approach is flexibility. The analytical approach delivers a closed form solution for capital allocation which reduces computing time and ease of implementation. This research demonstrates capital allocation provides a valuable tool for understanding the behaviour of capital relative to various risks. This enables insurers to better manage their risk exposure as they can start to see the drivers of risk.
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    A comparison of value at risk & expected shortfall models in cryptocurrencies
    (Stellenbosch : Stellenbosch University, 2023-03) Bosman, Lisa-Marie; Perrang, Justin; Stellenbosch University. Faculty of Economic and Management Sciences. Dept. of Statistics and Actuarial Science.
    ENGLISH SUMMARY: The key objective of this study is to examine the application of specific traditional market risk management measures on the cryptocurrency market and investigate the efficiency and accuracy thereof through the application of value at risk (VaR) and expected shortfall (ES) models. The further objective is to provide an extensive literature review of important topics relating to cryptocurrencies and the risk management thereof. Numerous studies and applications related to cryptocurrencies have already been conducted. This study clarifies certain aspects and factors regarding the cryptocurrency market, such as blockchains, cryptocurrency bubbles and the impending regulation of the asset class. As the volatile cryptocurrency market has become more prominent in the financial sector throughout the years, the modelling and management of market risk have become key areas related to the asset class. VaR and ES are well-known measures of market risk. These are implemented in this study on the daily return data for Bitcoin, Ethereum, Ripple and Dogecoin for the period 8 August 2015 — 31 August 2022. The historical simulation model, as well as independent and identically distributed (i.i.d.) models, assuming both normally and Student t distributed returns, are applied. The exponentially weighted moving average (EWMA) model provides an improvement upon the i.i.d. models. Following this, the asymmetric volatility of the data is taken into account with an adjusted EWMA model, the asymmetric exponentially weighted moving average (AEWMA). The final model applied is the filtered historical simulation (FHS), which combines the benefits of the historical simulation and AEWMA models using bootstrapping. The daily VaR and ES forecasts are extensively backtested to enable comparison among the models. The results produced differ among the different coins and for the different significant levels. However, it is clear that the asymmetric volatility of the data significantly impacts the results and must be accounted for in modelling. It can be concluded that traditional market risk management has an important place in the cryptocurrency market.