This thesis focuses on software fault detection in the telecom industry, which is crucial for companies like Ericsson to ensure stable and reliable software. Given the importance of software performance to companies that rely on it, automatically detecting faulty behavior in test or operational environments is challenging. Several approaches have been proposed to address this problem. This thesis explores reconstruction-based and forecasting-based anomaly detection using diffusion models to address software failure detection. To this end, the usage of the Structured State Space Sequence Diffusion Model was explored, which can handle temporal dependencies of varying lengths. The numerical time series data results were promising, demonstrating the model’s effectiveness in capturing and reconstructing the underlying patterns, particularly with continuous features. The contributions of this thesis are threefold: (i) A proposal of a framework for utilizing diffusion models for Time Series anomaly detection, (ii) a proposal of a particular Diffusion model Architecture that is capable of outperforming existing Ericsson Solutions on an anomaly detection dataset, (iii) presentation of experiments and results which add extra insight into the model’s capabilities, exposing some of its limitations and suggesting future research avenues to enhance its capabilities further. / Uppsatsen fokuserar på detektering av programvarufel inom telekomindustrin, vilket är essentiellt för företag som Ericsson för att säkerställa stabil och pålitlig programvara. Med hänsyn till vikten av programvarans prestanda för företag som är beroende av den är automatisk detektering av felaktigt beteende i test- eller operativa miljöer en utmanande uppgift. Flera metoder har föreslagits för att lösa problemet. Uppsatsen utforskar generativ-baserad och prediktiv-baserad anomalidetektering med hjälp av diffusionsmodeller för att hantera detektering av programvarufel. Den valda nätverksarkitekturen för att återskapa tidsseriedata var modellen ”Structured State Space Sequence Diffusion”. Resultaten för numeriska tidsseriedata var lovande och visade på modellens effektivitet i att fånga och återskapa de underliggande mönstren. Dock observerades det att modellen stötte på svårigheter vid hantering av kategoriska tidsseriekolumner. Begränsningarna i att fånga kategoriska tidsseriefunktioner pekar på ett område där modellens förmågor kan förbättras. Framtida forskning kan fokusera på att förbättra modellens förmåga att hantera kategoriska data på ett effektivt sätt.

The fashion industry is a significant contributor to greenhouse gas emissions and textile waste, prompting the need for sustainable practices. This thesis explores the use of diffusion models for generating synthetic data to enhance datasets used in machine learning, specifically focusing on second-hand fashion. Diffusion models, known for their ability to create high-quality images, offer potential solutions to the imbalance and quality issues in existing datasets. The study investigates how image generation and editing through diffusion models can improve datasets, the effectiveness of different prompting strategies, and the performance of synthetic data in machine learning models compared to real data. The methodology involves using the Kandinsky 2.2 inpainting model to generate and edit images, followed by manual and automated classification to evaluate image quality. Experiments demonstrate that diffusion models can plausibly improve dataset quality by adding and removing damage in images, although fully automating this process remains challenging. The results indicate that augmenting the datasets with synthetic images can potentially enhance the performance of the model, although the variability of the results suggests the need for further research. This thesis contributes to the field of sustainable fashion by proposing innovative methods for dataset augmentation using state-of-the-art generative models, aiming to support the development of efficient and automated sorting processes in the textile industry.

When a production company commits to creating a film based on a novel, it is essential that their team is equipped to manage the extensive responsibilities required to authentically translate the book to the big screen. This study aims to explore and address these challenges by utilizing contemporary Generative Artificial Intelligence technologies, including Large Language Models, Text-To-Speech, and Text-To-Image models. While recent advancements have focused on enhancing these models, there is a gap in research on their practical application and effectiveness in real-world scenarios. This research will detail the steps necessary to deconstruct a novel’s narrative and produce the final cinematic product. Additionally, it will propose novel methods to mitigate errors such as hallucinations generated by Language Models and image models, enhancing the fidelity and quality of the adaptations. iii

M.Sc. (Statistics)

M.Sc. (Statistics)

Value-at-Risk (VaR) model fails to predict financial risk accurately especially during financial crises. This is mainly due to the model’s inability to calibrate new market information and the fact that the risk measure is characterised by poor tail risk quantification. An alternative approach which comprises of the Expected Shortfall measure and the Lognormal Jump-Diffusion (LJD) model has been developed to address the aforementioned shortcomings of VaR. This model is called the Simulated-Expected-Shortfall (SES) model. The Maximum Likelihood Estimation (MLE) approach is used in determining the parameters of the LJD model since it’s more reliable and authenticable when compared to other nonconventional parameters estimation approaches mentioned in other literature studies. These parameters are then plugged into the LJD model, which is simulated multiple times in generating the new loss dataset used in the developed model. This SES model is statistically conservative when compared to peers which means it’s more reliable in predicting financial risk especially during a financial crisis. / Statistics / M.Sc. (Statistics)

In the present thesis we deal with several possible approaches to financial de- rivatives pricing. In the first part, we introduce the basic types of derivatives and the methods of trading. Furthermore, we present several models for the valuati- on of specific financial derivative, i.e. options. Firstly we describe Black-Scholes model in detail, which considers that the development of the underlying asset price is governed by Wiener process. Following are the jumps diffusion models that are extension of the Black-Scholes model with jumps. Then we get to jump models, which are based on Lévy processes. Finally, we will deal with the model, which considers that the development of the underlying asset price is governed by fractional Brownian motion with Hurst's coefficient greater than 1/2. All models are suplemented with sample examples. 1

In life insurance contracts, actuaries generally value premiums using deterministic mortality rates and interest rates. They have ignored them stochastically in most of the studies. However it is known that neither interest rates nor mortality rates are constant. It is also known that companies may encounter insolvency problems such as ruin, so the ruin probability need to be added to the valuation of the life insurance contracts process. Insurance companies should model their surplus processes to price some types of life insurance contracts and to see risk position. In this study, mortality rates and surplus processes are modeled and financial strength of companies are utilized when pricing life insurance contracts.

In this thesis, we investigate the potential of improving demand management activities in the global supply chains. In the increasingly global world, commerce is becoming more complex with an incredible amount of internal and external information available for businesses to select, analyze, understand and react. We identify opportunities for companies to convert data and business information into actionable intelligence. We first study the logistics industry with real data. In the Less-than-Truckload (LTL) market, we analyze an extensive historical shipment database to identify important factors to estimate LTL market rates. Quantifying critical expert knowledge, we develop a price estimation model to help shippers reduce their logistics cost and carriers to better manage their demand. In our second study, we analyze a global supply chain in the high tech industry. Using the demand dependency structure of certain products, we identify collaboration opportunities in the ordering practices that results in increased forecast accuracy. In our third study, we focus on using historical product adoption patterns for developing good pre-launch forecasts for new product introductions. Through a normalization approach and algebraic estimation procedures that use intuitive parameters, our models provide opportunities to significantly improve pre-launch forecast accuracy. Finally, in our fourth study, we develop novel approaches for modeling and mitigating the impact of demand seasonality in new product diffusion context. Focusing mainly on practical applications, our research shows that companies can find innovative ways for turning raw data into valuable insights leading to better demand management activities.

Doctor Scientiae - DSc / Robust Spectral Methods for Solving Option Pricing Problems by Edson Pindza PhD thesis, Department of Mathematics and Applied Mathematics, Faculty of Natural Sciences, University of the Western Cape Ever since the invention of the classical Black-Scholes formula to price the financial derivatives, a number of mathematical models have been proposed by numerous researchers in this direction. Many of these models are in general very complex, thus closed form analytical solutions are rarely obtainable. In view of this, we present a class of efficient spectral methods to numerically solve several mathematical models of pricing options. We begin with solving European options. Then we move to solve their American counterparts which involve a free boundary and therefore normally difficult to price by other conventional numerical methods. We obtain very promising results for the above two types of options and therefore we extend this approach to solve some more difficult problems for pricing options, viz., jump-diffusion models and local volatility models. The numerical methods involve solving partial differential equations, partial integro-differential equations and associated complementary problems which are used to model the financial derivatives. In order to retain their exponential accuracy, we discuss the necessary modification of the spectral methods. Finally, we present several comparative numerical results showing the superiority of our spectral methods.