In this study within quantitative portfolio optimization, stochastic programming is investigated as an investment decision tool. This research takes the direction of scenario based Mean-Absolute Deviation and is compared with the traditional Mean-Variance model and widely used Risk Parity portfolio. Furthermore, this thesis is done in collaboration with the First Swedish National Pension Fund, AP1, and the implemented multi-asset portfolios are thus tailored to match their investment style. The models are evaluated on two different fund management levels, in order to study if the portfolio performance benefits from a more restricted feasible domain. This research concludes that stochastic programming over the investigated time period is inferior to Risk Parity, but outperforms the Mean-Variance Model. The biggest aw of the model is its poor performance during periods of market stress. However, the model showed superior results during normal market conditions. / I denna studie inom kvantitativ portföljoptimering undersöks stokastisk programmering som ett investeringsbeslutsverktyg. Denna studie tar riktningen för scenariobaserad Mean-Absolute Deviation och jämförs med den traditionella Mean-Variance-modellen samt den utbrett använda Risk Parity-portföljen. Avhandlingen görs i samarbete med Första AP-fonden, och de implementerade portföljerna, med era tillgångsslag, är därför skräddarsydda för att matcha deras investeringsstil. Modellerna utvärderas på två olika fondhanteringsnivåer för att studera om portföljens prestanda drar nytta av en mer restrektiv optimeringsmodell. Den här undersökningen visar att stokastisk programmering under undersökta tidsperioder presterar något sämre än Risk Parity, men överträffar Mean-Variance. Modellens största brist är dess prestanda under perioder av marknadsstress. Modellen visade dock något bättre resultat under normala marknadsförhållanden.

<p>This thesis grew out of a problem encountered by a subsidiary of a Swedish multinational industrial corporation. This subsidiary is responsible for the corporation’s customer financing activities. In the thesis, we refer to these entities as the Division and the Corporation. The Division needed to find a new approach to finance its customer loan portfolio. Risk control and return maximization were important aspects of this need. The objective of this thesis is to devise and implement a method that allows the Division to make optimal funding decisions, given a certain risk limit. </p><p>We propose a funding approach based on stochastic programming. Our approach allows the Division’s portfolio manager to minimize the funding costs while hedging against market risk. We employ principal component analysis and Monte Carlo simulation to develop a multicurrency scenario generation model for interest and exchange rates. Market rate scenarios are used as input to three different optimization models. Each of the optimization models presents the optimal funding decision as positions in a unique set of financial instruments. By choosing between the optimization models, the portfolio manager can decide which financial instruments he wants to use to fund the loan portfolio. </p><p>To validate our models, we perform empirical tests on historical market data. Our results show that our optimization models have the potential to deliver sound and profitable funding decisions. In particular, we conclude that the utilization of one of our optimization models would have resulted in an increase in the Division’s net income over the past 3.5 years.</p>

This thesis grew out of a problem encountered by a subsidiary of a Swedish multinational industrial corporation. This subsidiary is responsible for the corporation’s customer financing activities. In the thesis, we refer to these entities as the Division and the Corporation. The Division needed to find a new approach to finance its customer loan portfolio. Risk control and return maximization were important aspects of this need. The objective of this thesis is to devise and implement a method that allows the Division to make optimal funding decisions, given a certain risk limit. We propose a funding approach based on stochastic programming. Our approach allows the Division’s portfolio manager to minimize the funding costs while hedging against market risk. We employ principal component analysis and Monte Carlo simulation to develop a multicurrency scenario generation model for interest and exchange rates. Market rate scenarios are used as input to three different optimization models. Each of the optimization models presents the optimal funding decision as positions in a unique set of financial instruments. By choosing between the optimization models, the portfolio manager can decide which financial instruments he wants to use to fund the loan portfolio. To validate our models, we perform empirical tests on historical market data. Our results show that our optimization models have the potential to deliver sound and profitable funding decisions. In particular, we conclude that the utilization of one of our optimization models would have resulted in an increase in the Division’s net income over the past 3.5 years.

The main aim of this thesis is to create a sequence of mathematical optimization models with different levels of complexity for the efficient management and waste energy utilization. Stochastic programming approach was utilized to deal with random demand and uncertain heating values. Hence, more applicable model of the waste-to-energy plant has been developed. As the next step, the model is enhanced by heating plant extension. Computations are realized for real-world data and optimal solution is found by using GAMS implementation.

The goal of this thesis is to explore a new clustering algorithm, VAE-Clustering, and examine if it can be applied to find differences in the distribution of stock returns and augment the distribution of a current portfolio of stocks and see how it performs in different market conditions. The VAE-clustering method is as mentioned a newly introduced method and not widely tested, especially not on time series. The first step is therefore to see if and how well the clustering works. We first apply the algorithm to a dataset containing monthly time series of the power demand in Italy. The purpose in this part is to focus on how well the method works technically. When the model works well and generates proper results with the Italian Power Demand data, we move forward and apply the model on stock return data. In the latter application we are unable to find meaningful clusters and therefore unable to move forward towards the goal of the thesis. The results shows that the VAE-clustering method is applicable for time series. The power demand have clear differences from season to season and the model can successfully identify those differences. When it comes to the financial data we hoped that the model would be able to find different market regimes based on time periods. The model is though not able distinguish different time periods from each other. We therefore conclude that the VAE-clustering method is applicable on time series data, but that the structure and setting of the financial data in this thesis makes it to hard to find meaningful clusters. The major finding is that the VAE-clustering method can be applied to time series. We highly encourage further research to find if the method can be successfully used on financial data in different settings than tested in this thesis. / Syftet med den här avhandlingen är att utforska en ny klustringsalgoritm, VAE-Clustering, och undersöka om den kan tillämpas för att hitta skillnader i fördelningen av aktieavkastningar och förändra distributionen av en nuvarande aktieportfölj och se hur den presterar under olika marknadsvillkor. VAE-klusteringsmetoden är som nämnts en nyinförd metod och inte testad i stort, särskilt inte på tidsserier. Det första steget är därför att se om och hur klusteringen fungerar. Vi tillämpar först algoritmen på ett datasätt som innehåller månatliga tidsserier för strömbehovet i Italien. Syftet med denna del är att fokusera på hur väl metoden fungerar tekniskt. När modellen fungerar bra och ger tillfredställande resultat, går vi vidare och tillämpar modellen på aktieavkastningsdata. I den senare applikationen kan vi inte hitta meningsfulla kluster och kan därför inte gå framåt mot målet som var att simulera olika marknader och se hur en nuvarande portfölj presterar under olika marknadsregimer. Resultaten visar att VAE-klustermetoden är väl tillämpbar på tidsserier. Behovet av el har tydliga skillnader från säsong till säsong och modellen kan framgångsrikt identifiera dessa skillnader. När det gäller finansiell data hoppades vi att modellen skulle kunna hitta olika marknadsregimer baserade på tidsperioder. Modellen kan dock inte skilja olika tidsperioder från varandra. Vi drar därför slutsatsen att VAE-klustermetoden är tillämplig på tidsseriedata, men att strukturen på den finansiella data som undersöktes i denna avhandling gör det svårt att hitta meningsfulla kluster. Den viktigaste upptäckten är att VAE-klustermetoden kan tillämpas på tidsserier. Vi uppmuntrar ytterligare forskning för att hitta om metoden framgångsrikt kan användas på finansiell data i andra former än de testade i denna avhandling

In autonomous driving, scenario generation can play a critical role when it comes to the verification of the autonomous driving software. Since uncertainty is a major component in driving, there cannot be just one right answer to a prediction for the trajectory or the behaviour, and it becomes important to account for and model that uncertainty. Several approaches have been tried for generating the future scenarios for a vehicle and one such pioneering work set out to model the behaviour of the vehicles probabilistically while tackling the challenges of representation, flexibility, and transferability within one system. The proposed system is called the Semantic Graph Network (SGN) which utilizes feedforward neural networks, Gated Recurrent Units (GRU), and a generative model called the Mixed Density Network to serve its purpose. This thesis project set out in the direction of the implementation of this research work in the context of highway merger scenario and consists of three parts. The first part involves basic data analysis for the employed dataset, whereas the second part involves a model that implements certain parts of the SGN including a variation of the context encoding and the Mixture Density Network. The third and the final part is an attempt to recreate the SGN itself. While the first and the second parts were implemented successfully, for the third part, only certain objectives could be achieved. / Vid autonom körning kan scenariegenerering spela en avgörande roll när det gäller verifieringen av programvaran för autonom körning. Eftersom osäkerhet är en viktig komponent i körning kan det inte bara finnas ett rätt svar på en förutsägelse av banan eller beteendet, och det blir viktigt att redogöra för och modellera den osäkerheten. Flera tillvägagångssätt har prövats för att generera framtidsscenarierna för ett fordon och ett sådant banbrytande arbete gick ut på att modellera fordonens beteende sannolikt samtidigt som utmaningarna med representation, flexibilitet och överförbarhet inom ett system hanteras. Det föreslagna systemet kallas Semantic Graph Network (SGN) som använder neurala nätverk, Gated Recurrent Units (GRU) och en generativ modell som kallas Mixed Density Network för att tjäna sitt syfte. Detta examensarbete riktar sig mot genomförandet av detta forskningsarbete i samband med motorvägssammanslagningsscenariot och består av tre delar. Den första delen involverar grundläggande dataanalys för den använda datamängden, medan den andra delen involverar en modell som implementerar vissa delar av SGN inklusive en variation av kontextkodningen och Mixture Density Network. Den tredje och sista delen är ett försök att återskapa själva SGN. Även om den första och den andra delen genomfördes framgångsrikt, kunde endast vissa mål uppnås för den tredje delen.