In this thesis three risk appetite indexes are derived and measured from the beginning of 2006 to the end of the first quarter in 2019. One of the risk appetite indexes relies on annualized returns and volatilities from risky and safe assets while the others relies on subjective and risk neutral probability distributions. The distributions are obtained from historical data on equity indexes and from a wide spectrum of option prices with one month until the options expires. All data is provided by Refinitiv through Öhman Fonder. The indexes studied throughout the thesis is provided by authors from financial institutions such as Bank of England, Bank of International Settlements and Credit Suisse First Boston. I conclude in this thesis that the Credit Suisse First Boston index and the Bank of International Settlements index generated the most intuitive result regarding expected response after major financial events. A principal component analysis demonstrated that the Credit Suisse First Boston index held most of the information in terms of explanation of variance. At last, the indexes was used as a trend-following strategy for asset allocation for switching between a safe versus a risky portfolio. A trend in the risk appetite was studied for 2 to 12 months back in time and resulted in that all of the risk appetite indexes studied throughout the thesis can be a helpful tool to asset allocation. / I denna rapport studeras tre riskaptit index från början av år 2006 till slutet av första kvartalet år 2019. Ett av riskaptit indexen är beroende av årlig avkastning och volatilitet hos flera olika riskabla och säkra tillgångar medan de andra två är beroende på subjektiva och risk neutrala sannolikhets-fördelningar. Fördelningarna erhålls från historisk data från olika aktieindex och från ett brett spektrum av options priser med en månad till optionerna förfaller. All data kommer från Refinitiv genom Öhman Fonder. Indexen som studeras i rapporten är ursprungligen härledda av författare från finansiella institut som Bank of England, Bank of International Settlements och Credit Suisse First Boston. I denna rapport kommer jag fram till att indexen från Credit Suisse First Boston och Bank of International Settlements genererar det mest intuitiva resultatet beträffande förväntningar efter större finansiella händelser. En principal komponent analys visade på att Credit Suisse First Bostons index innehöll mest information i form av förklaring av variansen. Tills sist så användes riskaptit indexen som en trendföljande strategi för tillgångsallokering mellan en säker och en riskfylld portfölj. Trenden i riskaptiten studerades från 2 till 12 månader bak i tiden och resultatet visar på att alla undersökta riskaptit index i denna rapport kan fungera som ett verktyg för tillgångsallokering.

In complex systems anomalous behaviors can occur intermittently and stochastically. In this case, it is hard to diagnose real errors among spurious ones. These errors are often hard to troubleshoot and require close attention, but troubleshooting each occurrence is time-consuming and is not always an option. In this thesis, we define two different models to estimate the underlying probability of occurrence of an error, one based on binary segmentation and null hypothesis testing, and the other one based on hidden Markov models. Given a threshold level of confidence, these models are tuned to trigger alerts when a change is detected with sufficiently high probability. We generated events drawn from Bernoulli distributions emulating these anomalous behaviors to benchmark these two candidate models. Both models have the same sensitivity, δp ≈ 10%, and delay, δt ≈ 100 observations, to detect change points. However, they do not generalize in the same way to broader problems and provide therefore two complementary solutions. / I komplexa system kan anomala beteenden uppträda intermittent och stokastiskt. I de här fallen är det svårt att diagnostisera verkliga fel bland falska sådana. Dessa fel är ofta svåra att felsöka och kräver noggrann uppmärksamhet, men felsökning av varje händelse är mycket tidskrävande och är inte alltid ett alternativ. I denna avhandling definierar vi två olika modeller för att uppskatta den underliggande sannolikheten för att ett fel uppträder, den första baserad på binär segmentering och prövning av nollhypotes, och den andra baserad på dolda Markovmodeller. Givet ett tröskelvärde för konfidensgraden är dessa modeller justerade för att utlösa varningar när en förändring detekteras med tillräcklig hög sannolikhet. Vi genererade händelser som drogs från Bernoullifördelningar som emulerar dessa avvikande beteenden för att utvärdera dessa två kandidatmodeller. Båda modellerna har samma sensitivitet, δp ≈ 10% och fördröjning, δt ≈ 100  observationer, för att upptäcka ändringspunkter. De generaliserar emellertid inte på samma sätt till större problem och ger därför två kompletterande lösningar.

The overall purpose of the PhD project is to develop a framework for making optimal decisions on the equity derivatives markets. Making optimal decisions refers e.g. to how to optimally hedge an options portfolio or how to make optimal investments on the equity derivatives markets. The framework for making optimal decisions will be based on stochastic programming (SP) models, which means that it is necessary to generate high-quality scenarios of market prices at some future date as input to the models. This leads to a situation where the traditional methods, described in the literature, for modeling market prices do not provide scenarios of sufficiently high quality as input to the SP model. Thus, the main focus of this thesis is to develop methods that improve the estimation of option implied surfaces from a cross-section of observed option prices compared to the traditional methods described in the literature. The estimation is complicated by the fact that observed option prices contain a lot of noise and possibly also arbitrage. This means that in order to be able to estimate option implied surfaces which are free of arbitrage and of high quality, the noise in the input data has to be adequately handled by the estimation method. The first two papers of this thesis develop a non-parametric optimization based framework for the estimation of high-quality arbitrage-free option implied surfaces. The first paper covers the estimation of the risk-neutral density (RND) surface and the second paper the local volatility surface. Both methods provide smooth and realistic surfaces for market data. Estimation of the RND is a convex optimization problem, but the result is sensitive to the parameter choice. When the local volatility is estimated the parameter choice is much easier but the optimization problem is non-convex, even though the algorithm does not seem to get stuck in local optima. The SP models used to make optimal decisions on the equity derivatives markets also need generated scenarios for the underlying stock prices or index levels as input. The third paper of this thesis deals with the estimation and evaluation of existing equity market models. The third paper gives preliminary results which show that, out of the compared models, a GARCH(1,1) model with Poisson jumps provides a better fit compared to more complex models with stochastic volatility for the Swedish OMXS30 index. / Det övergripande syftet med doktorandprojektet är att utveckla ett ramverk för att fatta optimala beslut på aktiederivatmarknaderna. Att fatta optimala beslut syftar till exempel på hur man optimalt ska hedga en optionsportfölj, eller hur man ska göra optimala investeringar på aktiederivatmarknaderna. Ramverket för att fatta optimala beslut kommer att baseras på stokastisk programmerings-modeller (SP-modeller), vilket betyder att det är nödvändigt att generera högkvalitativa scenarier för marknadspriser för en framtida tidpunkt som indata till SP-modellen. Detta leder till en situation där de traditionella metoderna, som finns beskrivna i litteraturen, för att modellera marknadspriser inte ger scenarier av tillräckligt hög kvalitet för att fungera som indata till SP-modellen. Följaktligen är huvudfokus för denna avhandling att utveckla metoder som, jämfört med de traditionella metoderna som finns beskrivna i litteraturen, förbättrar estimeringen av ytor som impliceras av en given mängd observerade optionspriser. Estimeringen kompliceras av att observerade optionspriser innehåller mycket brus och möjligen också arbitrage. Det betyder att för att kunna estimera optionsimplicerade ytor som är arbitragefria och av hög kvalitet, så behöver estimeringsmetoden hantera bruset i indata på ett adekvat sätt. De första två artiklarna i avhandlingen utvecklar ett icke-parametriskt optimeringsbaserat ramverk för estimering av högkvalitativa och arbitragefria options-implicerade ytor. Den första artikeln behandlar estimeringen av den risk-neutrala täthetsytan (RND-ytan) och den andra artikeln estimeringen av den lokala volatilitetsytan. Båda metoderna ger upphov till jämna och realistiska ytor för marknadsdata. Estimeringen av RND-ytan är ett konvext optimeringsproblem men resultatet är känsligt för valet av parametrar. När den lokala volatilitetsytan estimeras är parametervalet mycket enklare men optimeringsproblemet är icke-konvext, även om algoritmen inte verkar fastna i lokala optima. SP-modellerna som används för att fatta optimala beslut på aktiederivatmarknaderna behöver också indata i form av genererade scenarier för de underliggande aktiepriserna eller indexnivåerna. Den tredje artikeln i avhandlingen behandlar estimering och evaluering av existerande modeller för aktiemarknaden. Den tredje artikeln tillhandahåller preliminära resultat som visar att, av de jämförda modellerna, ger en GARCH(1,1)-modell med Poissonhopp en bättre beskrivning av dynamiken för det svenska aktieindexet OMXS30 jämfört med mer komplicerade modeller som innehåller stokastisk volatilitet.

No description available.

Markov chain is a mathematical tool for modeling systems that evolve over time and hasbeen used in many fields such as physics, chemistry, economics, biology, and data science.This thesis contains an introduction to the theory and the applications of Markov chains,focusing on those with finite state spaces. Starting with basic concepts and techniques, thetheory of Markov chains is comprehensively studied. The basic concepts covered includethe Markov property, transition matrix, higher order transition probabilities, classification of states, and Markov chains as graphs. The stationary distribution, its importancein probability theory, existence, and uniqueness of stationary distribution are then discussed, while the final part of the thesis deals with the simulations of Markov chains. Twoexamples are presented to illustrate the technique of Markov chain simulation, includinga weather prediction model and a DNA sequence model.

In the context of the significant expansion of e-commerce, Recommender Systems have become important tools for businesses, enhancing customer engagement through the personalization of product recommendations. This thesis investigates the integration of Reinforcement Learning concepts  into Supervised Learning frameworks, aiming to foster more accurate, novel and diverse recommendations. This study is conducted within the context of IKEA's Inspirational Feed, a  feed of home-furnishing inspirations provided across IKEA's digital platforms. For this purpose, a detailed analytical comparison of three different session-based, sequential recommendation models is executed. This includes the purely supervised GRU4Rec model, as well as two hybrid approaches — SQN and SMORL — which combine Supervised Learning with the Double Q-Learning algorithm from Reinforcement Learning. The primary focus lies on SMORL, a multi-objective model explicitly designed to enhance the diversity and novelty of recommendations. As the results of this analysis reveal, all three models were able to effectively learn interrelationships among IKEA's products and Inspirational Feed images and provided reasonable next image recommendations. However, no evidence was found that the incorporation of Reinforcement Learning in the learning process helped models to improve recommendations. The thesis concludes by proposing potential directions for future research and potential modifications to the experimental design that could possibly alter these findings.

For more than a year, COVID-19 has changed societies all over the world and put massive strains on its healthcare systems. In an attempt to aid in prioritizing medical resources, this thesis uses dynamic regression with ARIMA errors to forecast the number of hospitalizations related to COVID-19 two weeks ahead in Uppsala County. For this purpose, 100 models are created and their ability to forecast hospitalizations two weeks ahead for weeks 15-17 of 2021 for the different municipalities in Uppsala County is evaluated using root mean squared error (RMSE), mean absolute error (MAE), and mean absolute percentage error (MAPE). The best performing models are then utilized to forecast hospitalizations for weeks 19-22. The results show that the models perform well during periods of increasing numbers of hospitalizations during early 2021, while they perform less well during the last weeks of May 2021 where hospitalizations numbers have been falling dramatically. This recent decrease in forecasting performance is believed to be caused by an increase in vaccination coverage, which is not accounted for in the models.

Kernel methods are a well-studied approach for addressing regression problems by implicitly mapping input variables into possibly infinite-dimensional feature spaces, particularly in cases where standard linear regression fails to capture non-linear relationships in data. Therefore, the choice between standard linear regression and kernel regression can be seen as a tradeoff between constraints on the number of features and the number of training samples. Our results show that the Gaussian kernel consistently achieves the lowest mean squared error for the largest considered training size. At the same time, the standard ridge regression exhibits a higher mean squared error and lower fit time. We have proven algebraically that the solutions of standard ridge regression and kernel ridge regression are mathematically equivalent.

No description available.

In this thesis a method for generating option portfolios using machine learning, more specifically WGAN-GP (Wasserstein Generative Adversarial Networks with Gradient Penalty), is presented. To reduce the complexity however, the model does not immediately generate portfolios with option series, but instead option classes, which includes the underlying asset, option type and direction of position. The generated portfolios are then transformed such that they include option series. A comparison between the real and generated portfolios was conducted, using a range of different metrics, such as number of positions, total market value and margin. Which concluded in that the model, presented in this thesis, effectively functions as a portfolio generator.