The rise in renewable energy sources causes more imbalances in the power grid. These imbalances are handled on the secondary control reserve (SCR) market. The prices on the market are currently predominately determined by hydropower plants, making the market unattractive to potential market players. This thesis explores the development of a bidding strategy for these new players to enter the Swiss secondary control reserve (SCR) market. This is a sensitive matter, since bidding too high would result in the bid not being accepted, and bidding too low would mean a player could have earned more money.
Two products are traded on the SCR market: negative control reserve (NCR), activated in case of an overbalance of the grid, and positive control reserve (PCR), activated in case of an underbalance of the grid. To develop a bidding strategy, the NCR and PCR bidding prices were modelled by using an ARIMA model to forecast the next week’s maximum bid. The order of the model was selected by minimising the Akaike information criterion and the parameters were estimated by maximising the likelihood function. An ARIMA(1,2,1) model provided the lowest AIC score for both the NCR and PCR data.
The accuracy of the models was tested by examining the mean absolute error (MAE), the root mean squared error (RMSE) and the bias. To test the performance of the model on the SCR market, two additional metrics were introduced: the percentage of the bids accepted (PAB), and the percentage of the total potential revenue earned (PMR). Although the MAE, RMSE and bias of the ARIMA(1,2,1) models were low, the PAB and PMR were low as well. This is because both models tended to estimate the forecasts higher than the actual maximum prices, resulting in the bids not being accepted. By shifting the model down to the lower bound of the 95% one-step confidence interval, the PAB and PMR were more than doubled. Therefore, the forecasts of the shifted ARIMA(1,2,1) models, generated the best bidding price for the upcoming week.

This thesis proposes a new solution to minimize the number of batteries needed to schedule ships depending on the presented harbour. The proposed solution is an extension to the bin packing problem. Item Fragmentation (BPP-IF) and Conflicts (BPPC) were added to allow ships to carry more batteries and to prevent batteries from being scheduled for multiple ships, respectively. Negative Items (BPP-NI) were added to allow for the batteries to be charged when they were not scheduled to be used. The combination of the three bin packing extensions (BPPC-IF-NI) formed the basis for the proposed solution. By a polynomial time reduction we showed that BPPC-IF-NI is NP-hard and therefore cannot be analytically solved in polynomial time. The solution can be approximated with an updated version of the heuristic presented by Ekici (2022). The main idea in this heuristic approach is to generate a set of independent sets of the conflict graph and determine the packing of the bins using the independent sets with the help of the integer linear program ISB-IP. An iterative framework is used where 𝐿 sets of 𝑇 independent sets are generated at each iteration and considered together with the independent sets used in the best solution to obtain a better solution. After testing many possible combinations of 𝐿 and 𝑇, it was found that 𝐿 = 50 and 𝑇 = 10 gives the best results, meaning that half of the number of the initial independent sets (𝐿-value) containing a maximum of half the number of items in each set (𝑇-value) where added in each iteration. When using these parameters, it was found that the solution of the heuristic was the same as the true optimal value. This was checked by inserting the power set without conflicts into the ISB-IP. The performance of the proposed solution was tested on generated instances. It was seen that there is no correlation between the computation time and the number of conflicts. It was also found that there was a strong correlation between the number of conflicts and the number of batteries used in the solution, without any clear outliers. The proposed solution is able to very quickly approximate the minimum number of batteries needed to schedule the ships for the given harbour. Since most instances are approximated in a couple of seconds, it can also be used to update schedules when complication arise on a smaller scale. This would allow harbours to switch to electric ships, while reducing the cost by minimizing the number of expensive ship batteries.

In criminal investigations, individuals may be connected to illicit activities by linking their personal phone to an otherwise anonymous, crime-related phone. Several methods have been published that use cell tower registrations to differentiate between same-user and different-user scenarios for the two phones. However, criminals may deviate in movement patterns and phone usage from the test subjects on which the methods are developed and evaluated. Whether the proposed methods are robust to such different behavioral profiles is unclear. The scarcity of readily available datasets on criminals' movements and phone usage further complicates this issue.

Lacking precise knowledge of the behavior of the population of interest, we propose a robustness analysis. Here, we present a tool for generating synthetic datasets, based on well-established models for the movement of individuals. We used the tool to generate data for a range of behavioral properties, encompassing variations in both underlying movement and phone usage. We evaluated three existing methods using our synthetic data. The first is a discriminatory approach that learns typical movement patterns and phone usage from a reference dataset. The second approach uses a model of cell tower behavior, making minimal assumptions on user behavior by choosing pairs of registrations close in time. The third is a generic statistical method for comparing event data. Additionally, we present a fourth method that combines the latter two, as conceptually, they use different aspects of the data.

Our analysis reveals that the discriminatory method performs best in a baseline scenario but is most sensitive to behavioral deviations. The cell tower method shows the lowest baseline performance yet exhibits the strongest resilience to variations. The generic model appears intermediate in terms of performance and sensitivity. Given the importance of robustness in evaluating evidence, we recommend using the combined approach, which is both reliable and effective across our defined variations.

Intention aware routing system is a route-planning algorithm for electric vehicles that minimizes overall travel time by taking into consideration congestion at charging stations. This thesis extends this algorithm to allow choices to be made based on prices at charging stations. The goal of this thesis is to find a way to minimize maximum congestion while maximizing overall profit across the stations. To achieve this an optimal price has to be calculated. To this end, a formula is devised and applied to several graphs.

Automated Market Makers (AMMs) are a novel type of market makers that eliminate the need for a coun-terparty in a trade. This thesis analyses the properties of several types of AMMs, and in particular the con-centrated liquidity market maker. An axiomatic definition of AMMs is provided, and two types of constant function market makers (CFMMs), called the constant sum market maker (CSMM) and constant product market maker (CPMM), are explored. The concentrated liquidity market maker, which improves liquidity provision compared to the CPMM, is thoroughly analyzed, and it is shown that it’s trading function can be formulated as a composition of functions. This thesis also conjectures that the concentrated liquidity trading function can be approximated by taking an infinite number of compositions. Additionally, a simulation study is conducted using transaction mocking. The simulation study supports the conjecture, and brings several other noteworthy properties of the concentrated liquidity market maker to light.

This thesis provides a fresh perspective on the (vertex) integrity of graphs, serving as a measure of network robustness. The study begins by introducing fundamental concepts and methods for evaluating the integrity of different graph families. An Integer Linear Programming (ILP) model, specifically designed for assessing integrity, is then presented. By applying this model, integrity values are calculated for various graph families, and patterns within the results are identified. These patterns contribute to establishing boundaries or determining exact values of integrity for the analyzed graph families. The analyzed graph families encompass Glued Paths, generalized Theta graphs, (Double) Cone graphs, Fan graph, Lollipop graphs, generalized Barbell graphs, (Dutch) Windmill graphs, Paley graphs, and Kneser graphs. Additionally, two conjectures are formulated: one concerning a lower bound for the integrity of all Paley graphs, and another addressing the exact integrity values of specific Kneser graphs. The ILP model proves to be a valuable tool for further exploration of graph family integrity, offering opportunities for additional research and expanding our understanding of network robustness.

Facility location problems are an important set of problems within the field of optimisation. These problems consider which facilities to open out of a set of possible facilities and how to assign users to the open facilities. Most of the facility location problems studied have a linear objective. In this thesis, we consider a facility location problem with a quadratic objective, the Balanced Facility Location Problem (BFLP). This problem, and facility location problems in general, quickly becomes difficult to solve for standard MIP solvers as the input size increases. The difficulty of this problem is further supported by it being a NP-hard problem.

Hence, we develop three heuristics for the BFLP: two greedy heuristics and one local search heuristic. These heuristics are adapted from heuristics used for the standard Capacitated Facility Location Problem (CFLP).

The idea behind the first greedy heuristic is to close one facility at a time, starting with all facilities being open, until we have as many facilities open as the budget constraint of the BFLP dictates. At each step, the best facility to close is closed. Apart from adapting this heuristic to accommodate the slightly different constraints of the BFLP, we also make some further adjustments in order to reduce the running time.

The second heuristic that we adapt is a heuristic that instead of closing facilities one at a time, opens facilities one by one, until we reach the budget of open facilities that the BFLP allows. These simple heuristics perform very well in practice on both small and large instances of the BFLP.

Lastly, we discuss a local search heuristic, which attempts to improve a solution to the BFLP by opening one facility and closing another facility at each iteration. The local search only improves marginally upon the results of the greedy algorithms.

For use within the heuristics for the BFLP, we require fast heuristics to solve a subproblem of the BFLP, the problem of assigning users to facilities where the set of open facilities is fixed. Hence, we develop three heuristics for this subproblem and also adapt a previously developed heuristic to be optimised for its use within the BFLP heuristics.

Our heuristics achieve results that are similar or better than what a MIP solver achieves and find a good solution in significantly less time. Especially when the MIP solver struggles, due to the size or limited capacity of the BFLP instance, our heuristics are able to outperform the MIP solver.

This thesis focuses on a problem formulated by Claude Shannon named the Shannon capacity. This problem is about information rate per time unit over a noisy channel. The noisy channel is here represented by a graph. We specifically focus on a class of circulant graphs that are denoted by C(n,k) with vertex set z/nz, where all vertices are connected with the k-1 vertices before and after it. We will discuss upper bounds that were found for the Shannon capacity and how C(n,k) behaves with these upper bounds. After that we will focus on multiple ways to calculate lower bounds for the Shannon capacity of $C(n,k)$. For these three search methods will be used. These are exhaustive searching for optimal values, optimal ways to make packagings and solutions created by using a special form. As last the answers will be discussed by combining the upper and lower bounds for C(n,k). From this conclusions are drawn after which some possibilities will be given for further research. 

In this report, I investigate strategic decision making in the Formula E racing series for Porsche. Formula E is an electric car circuit racing series, where the main tasks of race strategy are allocating energy consumption across the race and timing mandatory "attack mode" activations (similar to small-scale pitstops). I work on a flawed existing tool that simulates Formula E races with the goal of identifying optimal strategies. By learning from Porsche's experience and comparing the tool against related literature, I investigate how to model a Formula E race.

To do this, I outline a method to measure the realism of our simulated races. By defining a race as a set of stochastic processes approximated with empirical data, I find a dissimilarity metric for the underlying probability distributions of two collections of races. My dissimilarity metric is based on Kantorovich's formulation of the optimal transport problem as applied to probability measures. The cost function used within this dissimilarity metric is based on how differently two drivers' individual races evolve from start to end, using gaps between times of arrival.

I introduce various alterations to the race model, based on experience and related literature. Through applying my metric to different versions of my race model, I evaluate these alterations and find improvements. Doing so shows measurable gains in the race model were achieved; this is also checked by measuring the prediction error of simulations versus the true observed race.

My approach yields a scalar metric that allows fast and straightforward tuning of any race model. It uses a high degree of aggregation to successfully compare otherwise not trivially comparable data. While already delivering a significantly improved model, my dissimilarity metric in conjunction with the prediction error-based metrics can help to find further improvements in the future. This is also independent of the used simulation method or format, since my metric only requires realisations of true and simulated races as input.

This thesis is about pricing European options using a Fourier-based numerical method called the COS method under the rough Heston model. Besides examining the efficiency and accuracy of the COS method for pricing options under the rough Heston model, it is also investigated if the rough Heston model produces the advantages of the so-called rough volatility models. To do so, the characteristic function of the rough Heston model is derived, and the COS method for the rough Heston model and also a Monte Carlo simulation scheme is introduced. Throughout the thesis, the theoretical background of the rough Heston model, the numerical techniques and some numerical experiments on European option prices and implied volatility behaviors are presented. Also, a calibration of the rough Heston model is performed using Artificial Neural Networks. As a result of this thesis, pricing of European options using COS method is succeeded. Moreover, it is shown that the rough Heston model produces the rough volatility behaviors as expected.

This thesis presents an insight in the Riemann zeta function and the prime number theorem at an undergraduate mathematical level. The main goal is to construct an explicit formula for the prime counting function and to prove the prime number theorem using the zeta function and a Tauberian theorem. The Riemann zeta function can be continued analytically to the whole complex plane except at s = 1. Two proofs of this continuation were given by Bernhard Riemann in his famous article ``Ueber die Anzahl der Primzahlen unter einer gegebenen Grösse'' from 1859. Those proofs are studied in detail in this thesis after introducing all the required foreknowledge on the gamma function. The prime counting function π(x) counts the number of primes less than or equal to x. An explicit formula for π(x) in terms of the nontrivial zeros of the zeta function will be constructed in a similar way as Riemann did in his article. Finally, the prime number theorem will be proved. This theorem describes the asymptotic distribution of the primes among the natural numbers. Using the analytic continuation of the zeta function and a Tauberian theorem, the prime number theorem can be proved quite easily with only basic theory from complex analysis.

Cooperative game theory studies multi-agent environments where agents are able to make binding agreements. A lot has been written about dividing goods or other positive gains among the agents. This study investigates ways to distribute tasks with a negative utility in a strategyproof way. The intended application is a group of people or companies who can distribute such tasks between them to benefit from each other. The agents value tasks being done, but would rather not do it themselves. They can however, distribute the tasks to mutually benefit. Agents value tasks differently and also have different costs for them. This study investigates the theoretical properties of this problem. Particularly, we look at the Core, which is the set of solutions where agents have no incentive to form coalitions between them and ignore the result of the mechanism. Then, two algorithms are proposed to solve the problem. Finally, experiments are done to predict what results would occur in practice.

Recent studies in game-theory provided ways to steer multi-agent games to their Nash equilibrium by means of a decentralized approach. However, these approaches have not considered the internal dynamics of the individual agents. This thesis work provides decentralized control methods to account for these internal dynamics whilst ensuring that the overall system still reaches the Nash equilibrium.

This thesis captures the calibration of a FX hybrid model: The FX Black-Scholes Hull-White model. The main focus is on the calibration of the parameters in the Hull-White process: The mean reversion and the volatility parameter. The latter is commonly calibrated as a time-dependent parameter, whilst the mean reversion parameter is not. This thesis covers the calibration of the mean reversion as a time-dependent parameter. A known method from the Literature is researched, where we calibrate the mean reversion independently from the volatility parameter to the ratio of two swaptions with the same expiry but different tenor. In our research this method is extended to the negative interest rate environment by assuming that the swap rate follows a shifted lognormal distribution instead of a lognormal distribution. We show that a specific set of swaptions can be chosen, so that the calibration problem is simplified. This choice leads to sequential calibration of convex optimization problems. Numerical results of calibration to artificial and market data are presented, where we compare our method to picking the mean reversion parameter arbitrarily. The findings suggest that the choice of mean reversion parameter affects the calibration procedure. Therefore, we argue that a calibration method for the mean reversion would be appropriate. Besides the focus on the Hull-White process, the calibration of the volatility parameter in the FX Black-Scholes process of the hybrid model is investigated. For the calibration of the FX volatility parameter ATM options on FX rates are used. Numerical results of calibration to artificial and market data are shown. A typical problem of calibration in the industry is discussed: Precision for late maturities. The results in this thesis suggest that this problem could be solved. For research on homogeneity constraints on the time-dependent parameters, the performance of delta-hedging is investigated. The delta-hedging is performed in a simple Black-Scholes world with time-dependent volatility. We show that given a fixed amount hedges beforehand and interest rate zero, there exists an optimal distribution of time points that will lead to equal variance on the profit and loss for every volatility function that has equal implied volatility from t0 to maturity T. Using this strategy, the homogeneity of the volatility parameter has no impact on the performance of delta-hedging. Therefore, in this thesis no homogeneity constraints are used for the calibration of the time-dependent parameters.

This thesis deals with different models for decision-making under risk in financial applications, mainly models that incorporate irrational human behavior. First of all, traditional expected utility theory is considered. Hereafter, two models that incorporate irrational human behavior are discussed and compared: prospect theory and cumulative prospect theory. Next, these models are applied to option pricing. The influence of various levels of sentiment on the option price is investigated and the prices are compared with Black-Scholes prices. Also, a sensitivity analysis is done in order to investigate the influence of the prospect parameters on the option price. Furthermore, the different models discussed are applied to portfolio management for which the optimal wealth profiles are analyzed and compared. Moreover, a data analysis with a portfolio of stocks of different indices is done in which it is investigated whether the parameter estimates used for prospect sentiment are applicable to financial data. Finally, a hedge test under prospect sentiment is performed in order to investigate whether a delta-hedge leads to sufficient results in case of asset price paths under prospect sentiment.

This thesis adds to quantitative literature on terrorism by examining the relationship between various annual country statistics and the number of terrorist attacks. In addition, it assesses the potential of forecasting terrorism. Combining an extensive review of literature from social science, with data analysis of the Global Terrorism Database, results in a specific selection of attacks on country-level, along with various factors that allegedly affect terrorism. It is shown that, under certain conditions, the countries can be fit by a nonhomogeneous Poisson process model with a Weibull baseline intensity and a piecewise constant covariates component. For three out of five countries, the in-sample results are satisfactory, providing a tentative answer to the general debate whether terrorism can be explained by root causes. Out-of-sample results for Afghanistan and Somalia are promising for future research and implementation in policy making.

This thesis is about pricing European options and forward start options under the Heston LSV model. The impact of conditionally calibrating the Heston parameters on the satisfaction of the Feller condition and thereafter correcting with a local volatility surface is investigated here. The results show that this approach is computationally time efficient and accurate. Efficient numerical approaches for this LSV model, such as the multilevel Monte Carlo method, are also investigated. Furthermore, a comparison of several discretizations schemes for the SV part have been conducted. For the calibration of the local volatility surface, the efficiency of the Particle method and the Bin method are compared. An alternative numerical approach to this problem which builds on these two methods is developed and tested.