Correlation matrices play a central role in multivariate modelling across fields such as finance and statistics. However, generating valid correlation matrices, remains a non-trivial problem due to the global positive definiteness condition they must satisfy. This thesis investigates two methods for generating correlation matrices, with extensions on how to control or influence the average correlation. The first method relies on square root decomposition of the correlation matrix, parametrizing it as the product of a matrix with unit-norm rows and its transpose. A recent extension of this by Tuitman et al. is explored, which enables the generation of matrices with a fixed average correlation. This is achieved through iterative construction of the decomposition, ensuring the weighted sum of vectors has a prescribed norm, corresponding to the target average correlation. The algorithms geometric structure, feasibility conditions, and statistical properties are analysed.
The second method is based on the C-vine construction using partial correlations, as introduced by Joe and Kurowicka. There exists a one-to-one mapping from a set of partial correlations to a full correlation matrix. This approach parametrizes the matrix through a structured sequence of partial correlations. The distribution from which these partial correlations are sampled can be adjusted to achieve specific properties in the resulting matrices, for example using specific Beta distributions we obtain matrices following the LKJ distribution. The extension by Joe and Kurowicka is investigated, which allows the expected value of each correlation to be fixed across samples.
A comparison of both methods is provided in terms of construction, flexibility, numerical stability, and statistical properties of the resulting matrices. While the square root decomposition method offers strict per-matrix control over the average correlation, the C-vine approach provides greater flexibility, enabling finer control over marginal distributions. The thesis concludes with a discussion on practical trade-offs and potential directions for future work.

This report evaluates methods for reconstructing the coefficients of a model that describes the relationship between environmental conditions and the performance of potato genotypes, with performance measured by the weight of storage organs. For each genotype, this relationship is modeled as a linear combination of environmental factors weighted by genotype-specific environmental coefficients. The model incorporates the soil moisture field effect, wich varies both over the growing season and spatially within the field, with the latter captured through a linear combination of basis functions weighted by field effect coefficients. Initially, synthetic environmental data is generated, and fixed field effect and genotype-specific environmental coefficients are established. The model then calculates the expected performance based on these coefficients.

Subsequently, two approaches — a two-step method and a one-step method — are tested to reconstruct the original coefficients using the environmental and performance measurements. The robustness of both methods to noise is evaluated, and the minimum required number of environmental measurement locations within the field, as well as the optimal number of intermediate harvests during the growing season, are determined.
This is important because, once refined and expanded, the model and reconstruction methods can be applied to real multi-environment data to provide insights into how environmental factors influence the growth of different genotypes. Such analyses are important for advancing plant breeding efforts.

Aircraft operations require careful balance between maintaining sufficient crew availability and managing costs effectively. At KLM, current static methodologies for reserve crew planning achieve a 42.8% prediction accuracy on average, leading to either costly overstaffing or potentially disruptive understaffing. This research addresses this operational challenge by investigating the central question: ”How can we develop a self-learning model that enhances the prediction of reserve crew demand in the aviation industry by considering key factors such as seasonal variations and sickness absence patterns?”

Our literature review revealed a significant gap in current research. While studies have explored various aspects of airline operations and crew management, few have addressed the specific challenge of predicting reserve crew demand through machine learning approaches. The literature particularly lacked understanding of how multiple predictive factors interact and how illness patterns impact crew availability.

The research methodology involved systematic analysis of operational data from KLM spanning January 2013 through December 2023, focusing on the Boeing 777/787 fleet and Captain rank. We developed an integrated prediction framework comprising three main components: illness pattern analysis, reserve demand modelling, and operational validation. After evaluating multiple approaches including neural networks (LSTM, CNN) and traditional time series models, we identified an ARIMA(2,1,1) model with exogenous variables as optimal, based on both statistical criteria and operational requirements.

Analysis revealed previously undocumented relationships between operational factors, notably stronger correlation between incidental illness and reserve demand (r = 0.780) compared to structural illness patterns (r = 0.666). The developed model achieved 93% prediction accuracy, translating to conservative cost savings of €3.15 million in the first three quarters of 2024 through improved resource allocation and prevented flight cancellations. The model demonstrated particular strength in capturing dynamic patterns, successfully predicting major disruption events including an unexpected global illness wave in April 2024.
While the implementation shows promise for transforming reserve crew planning, several important challenges and areas for future research remain. The model’s reliance on historical patterns creates potential vulnerability to structural changes, and maintaining consistent data quality across systems presents ongoing challenges. Additionally, the impact of pilot preferences on reserve usage represents a complex system that warrants dedicated future research, as these preferences can significantly influence reserve crew utilization patterns. Despite these limitations, the system has reached implementation maturity, with KLM planning to utilize it for 2025 reserve capacity determinations.

This research establishes new possibilities for airline resource management while providing a framework for similar applications across the aviation industry. The findings suggest that machine learning approaches can significantly enhance prediction accuracy, though careful consideration must be given to operational constraints and data quality requirements. Future research opportunities include investigating more sophisticated approaches to handling extreme events, exploring the integration of additional predictive factors such as weather patterns and Not Fit to Fly data, and developing comprehensive models to account for pilot preferences and their impact on reserve crew demand.

Electronic trading algorithms are at the centre of every buy-side equity trading desk. These algorithms rely often on market impact models, which are stochastic models for the stock prices that account for the feedback effects of trading. Propagator models are central tools for describing the evolution of market impact during and after a trade. This thesis extends the linear propagator model by proposing a new variant that incorporates time-varying liquidity and general decay kernels. To bridge the gap between theory and practice, we use Robeco's proprietary order data base to calibrate the model and validate its performance. The main findings reveal a two-stage decay pattern of market impact, the absence of a single best admissible decay kernel, and a model performance which is in line with our expectations based on the low-signal to noise ratio of the data. The main application of the model in this research is its use in the optimal execution problem, in both a intraday and multiday setting. In an intraday setting we formulate the problem for a risk aware trader and incorporate short-term alpha signals. The discrete analogs of these problems are solved analytically and we highlight significant cost reduction compared to industry benchmarks. In the multiday framework, we quantify the expected cost of trading two adjacent orders and use this to find optimal multiday execution strategies. In a final simulation study we quantify the expected cost of rebalancing two similar investment accounts on consecutive days with a varying number of overlapping stocks. The simulation study accentuate a significant additional cost for the account trading on the second day, which stresses the importance of multiday cost management in rebalancing investment accounts.

This paper addresses the challenge of accurately monitoring power cable temperatures, which is crucial for the reliability and efficiency of electrical power systems during the energy transition. Overheating of power cables can lead to insulation failure and reduced lifespan, making precise temperature monitoring essential. Recent research by Alliander has explored the use of electromagnetic reflectometry for the recon- struction of power cable temperatures by analyzing the propagation time of pulsed electromag- netic signals within the cable. This study aims to improve upon this by directly reconstructing the electromagnetic parameters of the power cable and understanding their temperature depen- dence through a controlled experiment. Key steps include: • Cable Modeling: Using the Telegrapher’s equations to describe voltage and current distri- butions in the time and frequency domains. • Data Transformation: Converting these equations into integral equations and discretizing them to define an inverse scattering problem. • Experimental Validation: Using synthetic data and data from a temperature-controlled experiment by Alliander to test and refine the reconstruction method The study reconstructs the electrical parameters of the cable and attempts to find a relation between the parameters and the cable temperature. This method attempts a more accurate temperature monitoring system, enhancing the safety and efficiency of power grids

This thesis explores the application of Gaussian Graphical Models (GGMs) with a specific focus on identifying symmetries within EEG data. A significant challenge in using GGMs is achieving accurate estimations with limited observations, which is common in medical data. This research proposes a methodology for detecting and integrating symmetric structures in GGMs, thereby reducing the number of parameters and improving model interpretability. We follow developments presented by Højsgaard en Lauritzen (2008).
The study includes a detailed explanation of the multivariate Gaussian distribution, Maximum Likelihood Estimation (MLE), and the implementation of Iterative Partial Maximization for parameter estimation. Additionally, hierarchical clustering is employed to systematically identify symmetry classes. Results indicate that incorporating symmetry constraints enhances the accuracy and interpretability of GGMs.
The research shows that symmetry constraints simplify models, making them more robust and easier to understand.
A simulation study was conducted to test the efficiency and accuracy of the developed algorithm for symmetry detection. The findings from these simulations validate the proposed approach, demonstrating significant improvements in model performance.
Finally, the methodology was applied to an EEG dataset, highlighting practical applications in neuroscience. The results from the EEG data analysis further confirm that symmetry constraints can reveal underlying patterns in brain connectivity, offering valuable insights into the neural dynamics.
This thesis contributes to the existing literature by providing a systematic approach to detect symmetries in high-dimensional data models, particularly its practical utility with real-world EEG data.

In forensic science, the strength of evidence is calculated mainly by statistical models called likelihood ratio systems. In court cases, the specific-source likelihood ratio system is used by forensic scientists to determine if a trace originates from a known reference, called the trace-reference problem. However, collecting sufficient data to create a specific source model may be time-consuming and costly. If the number of court cases becomes too high this could be problematic. Therefore there is a need for other models that can perform as well as a specific-source model if it is infeasible.

A common-source model could be a solution, as this model can be re-used over cases. To this end, we introduce two common-source systems: a common-source feature-based system and a common-source score-based system. We compare their performance to a specific-source score-based system in a trace-reference setting. The simulations show that the common source feature-based method is the best-performing likelihood ratio system if the dimensionality is not too high, and the sources are equally variable. The analysis shows that the common-source score-based method can work as effectively as a specific-source score-based model in certain scenarios.

Additionally, we researched a preprocessor, known as percentile rank, which aims to consider typicality for score-based methods. For the common-source score-based system, using a percentile-rank preprocessor can improve the performance for large sample sizes, while considering the rarity of the measurements.

Banks issue mortgages with an embedded option for borrowers to prepay a part of the loan. However, this behaviour poses a risk to banks as it disrupts the level and timing of mortgage cash flows. From an earning perspective, when interest rates decrease, customers are financially incentivised to prepay their mortgages, resulting in a decrease in the bank’s income when the cash proceeds are reinvested at a lower rate. Conversely, from a value perspective, with an increase in interest rates, reducing the financial incentive to prepay, cash flows are moved further ahead in time, thereby increasing the duration of the mortgage. These two scenarios highlight the instability in the bank’s margin and value caused by prepayments. To address this risk, banks employ hedging strategies to mitigate the prepayment risk and achieve margin and value stability. This research aims to identify an effective hedging strategy that can accomplish both.

The research utilised the one-factor Hull-White model to simulate various interest rate scenarios, while an interest rate-dependent logistic prepayment model provided monthly prepayment rates based on the mortgagors’ refinancing incentives. Ten different hedging techniques were explored, including the internal funding, a static and dynamic notional hedge, and a static and dynamic value hedge. Additionally, a calibrated receiver swaption was included in each of these five hedging approaches. Subsequently, each of these hedging approaches was assessed for its margin stability, measured by the variance of the net interest margin, and its value stability, evaluated through the variance of the net present value, the average basis point value, and the NPV-at-Risk in ±200 basis point shocked interest rate scenarios.

The analysis indicated that relying solely on internal funding performs poorly in terms of both margin and value stability. Dynamic hedges were found to generally outperform their static counterparts, due to their ability to respond to market changes. Furthermore, the notional hedge demonstrates superior margin stability, while the value hedge exhibits the best value stability. Additionally, the analysis revealed that the incorporation of a receiver swaption significantly improves the NPV-at-Risk but has limited impact on the other risk metrics. Based on the conducted research, it is concluded that for a bank aiming for both value and margin stability, the most effective hedge strategy is the dynamic value hedge without the utilisation of a swaption. However, it should be noted that the ultimate choice for a hedging strategy depends heavily on the risk appetite of each bank. If a bank prioritises attaining margin stability, the recommended choice would be the dynamic notional hedge without the incorporation of the receiver swaption. On the other hand, for a bank that prefers value stability over margin stability, the dynamic value hedge without the inclusion of a swaption should be considered. Moreover, the final decision may also be influenced by mandatory requirements imposed by financial regulators, such as the European Central Bank.

This thesis investigates the application of neural stochastic differential equations (NSDEs) in financial modeling. It begins by presenting existing theoretical interpretation of NSDEs and investigates the properties of their solutions. By establishing a solid foundation, the thesis sets the stage for further explorations. A significant focus of the research is on the calibration and joint calibration of options using Markovian-type neural SDEs. This modeling approach is carefully chosen after conducting an extensive analysis that considers both the supporting evidence for the rough volatility hypothesis and the counterarguments in favor of Markovian volatility models. By undertaking a thorough study of these perspectives, the thesis aims to provide an in-depth understanding of the advantages and disadvantages associated with each modeling approach.
Additionally, the thesis addresses the challenge of data scarcity, a common issue faced in financial research. Recognizing the limited availability of real-world data and its potential impact on model development and testing, the research explores various existing methods for generating synthetic financial data.

Recent advancements in causal inference and machine learning research have brought forward methods to estimate effects of interventions from observational data. The augmented inverse probability weighted (AIPW) estimator is such a method, which can be used to obtain estimates of potential outcomes. Potential outcomes are defined as a hypothetical outcome pair {Y⁽¹⁾,Y⁽⁰⁾}, of which only one outcome is observed in the data. Estimation of intervention effects boils down to effectively estimating these potential outcomes.
Using the AIPW estimator, we aim to evaluate the average effect of increasing the energy efficiency of houses in the Netherlands on their expected transaction price. Moreover, we investigate how this expected effect changes when we condition on a certain subset of the data.
Given that our assumptions hold, we find that on average, the estimated expected increase in transaction price is positive when improving the energy efficiency of a house. Improving an energy inefficient house to moderately energy efficient is expected to increase the transaction price by approximately €97.70,- per m², while the improvement from moderately energy efficient to energy efficient increases the expected transaction price by approximately €20.96 per m².  In general, older, smaller and more energy inefficient houses increase most in expected transaction price per m² when their energy efficiency is improved.

In the fight against money laundering, demand for data-driven Anti-Money Laundering (AML) solutions is growing. Particularly anomaly detection algorithms have proven effective in the detection of suspicious customer behaviour, as well as observing patterns otherwise hidden in customer transaction data. In this thesis, the Isolation Forest anomaly detection algorithm is studied in combination with the model-specific local explanation method, Multiple Indicator Local Depth-based Isolation Forest Feature Importance (MI-Local-DIFFI). To expand Isolation Forest to mixed-attribute data sets, the incorporation of nominal features is explored in more detail. This analysis resulted in the introduction of Isolation Forest with Categorical Sampling (iForestCS ), a methodology that directly incorporates nominal attributes into an isolation tree without the need of encoding it onto a numerical scale. This method is tested against different encoding strategies and Isolation Forest Conditional Anomaly Detection (iForestCAD) using different synthetic data sets. The method shows improved performance to the utilization of encoding strategies for different parameters of the underlying synthetic data. Furthermore, this thesis explores the potential of ternary Isolation Forest, in which the branching strategy of an isolation tree is expanded to produce three child nodes. It is demonstrated using synthetic data, that particularly the performance of MI-Local-DIFFI reduces when applied to a ternary Isolation Forest. Finally, the research considers a practical use-case. Using customer transaction data from Triodos Bank, the locally explainable Isolation Forest is applied to mixed-attribute customer transaction data. This has provided useful insight and resulted in the detection of suspicious customer behaviour and the introduction of new rules into business practices. Although the most interesting customer behaviour did not directly emanate from the nominal attributes, the method of incorporating nominal features resulted in differences when considering the anomalies with the highest anomaly scores.

Machine learning methods like outlier detection are becoming increasingly more popular as tools in the fight against money laundering. In this thesis, we analyse the Isolation Forest outlier detection algorithm in detail and introduce a new local explanation method for Isolation Forest, the MI-Local-DIFFI (Multiple Indicator Local-DIFFI) method. The method uses the structure of the isolation trees and the traversal of individual outliers down the trees to determine an importance weight for each of the features. These weights are then combined into feature importance scores that are used to explain why a specific outlier is identified as such. In anti-money laundering (AML), such explanations are very valuable when determining whether an outlying customer is suspicious or not. MI-Local-DIFFI is based on a global explanation method called DIFFI and while we were conducting our research, another local version, Local-DIFFI, was also introduced. In the thesis, we use a synthetic data set to compare the performance of four different explanation methods including our MI-Local-DIFFI, Local-DIFFI and the state-of-the-art TreeSHAP method. Our MI-Local-DIFFI shows excellent results in terms of performance and runtime. Furthermore, we use a data set from Triodos bank to apply the explainable outlier detection methodology consisting of the combination of Isolation Forest and MI-Local-DIFFI. This resulted in interesting findings like the revealing of data quality issues in the current system and references to EDRs and SARs. However, after further inspection, no SARs were filed but some customers were put to higher risk classes. This procedure will be performed on a monthly basis with the goal of continuing to improve the AML processes of the bank.