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This project has three parts. The first part is to use the efficient frontier and find the tangency portfolio to form our optimal portfolio. We built our portfolio using the Interactive Brokers software and rebalanced every week for 4 holding periods to see the relationship between our projected returns and actual market returns. In the second part we considered the Capital Asset Pricing Model (CAPM) and ran linear regressions on the stocks we chose in the first part of the project. This process is based on our idea of finding the systematic risk in each stock to improve our stock choosing ability. In the last part we introduce the concept of factor models and add more factors into our original CAPM model. Via a back-testing method, we test the reasonability of our factors and give advice to further improve our portfolio optimization project.

Master of Science in Engineering - Engineering / Various methods, mostly statistical in nature have been introduced for stock market modelling and prediction. These methods are, however, complex and difficult to manipulate. Computational intelligence facilitates this approach of predicting stocks due to its ability to accurately and intuitively learn complex patterns and characterise these patterns as simple equations. In this research, a methodology that uses neural networks and Bayesian framework to model stocks is developed. The NASDAQ all-share index was used as test data. A methodology to optimise the input time-window for stock prediction using neural networks was also devised. Polynomial approximation and reformulated Bayesian frameworks methodologies were investigated and implemented. A neural network based algorithm was then designed. The performance of this final algorithm was measured based on accuracy. The effect of simultaneous use of diverse neural network engines is also investigated. The test result and accuracy measurements are presented in the final part of this thesis. Key words: Neural Networks, Bayesian framework and Markov Chain Monte Carlo

Tese de mestrado. Engenharia Electrotécnica e de Computadores (Especialização em Energias Renováveis). Faculdade de Engenharia. Universidade do Porto. 2007

The game of Cribbage has a complex way of counting points in the hands that are dealt to each player. Each player has a choice of what cards to keep and what cards to throw into an extra hand, called the crib, that one of the players gets to count towards his score. Ideally, you could try to keep the most points possible in your hand and your crib, or, conversely, the most points in your hand with the fewest points in your opponent’s crib. To add to the fun, a final card is randomly chosen that all three hands share. This thesis deals with finding optimal expected values for each player’s hand and the crib. Unfortunately, finding the exact optimal values is very difficult. However, I have managed to get bounds on the optimal values.

Congestion and oversaturated roads pose significant problems and create delays in every major city in the world. Before this problem can be addressed, we must know how much traffic is flowing over the links in the network. We transform a road network into a directed graph with a network flow function, and ask the question, “What subset of vertices (intersections) should be monitored such that knowledge of the flow passing through these vertices is sufficient to calculate the flow everywhere in the graph?” To minimize the cost of placing sensors, we seek the smallest number of monitored vertices. This is known as the Sensor Location Problem (SLP). We explore conditions under which a set of monitored vertices produces a unique solution to the problem and disprove a previous result published on the problem. Finally, we explore a matrix formulation of the problem and present cases when the flow can or cannot be calculated on the graph.

L'orientation des telecommunications vers les hauts-debits fait de la technique de modulation OFDM l'un des centres d'intérêts privilégies de la recherche actuelle. Cette technique basée sur le principe d'orthogonalité des "filtres" réalisant la modulation ne nécessite pas d'égalisation a proprement parler, mais requiert une estimation de la réponse fréquentielle du canal pour chaque symbole transmis. Les contextes de propagation rencontres aujourd'hui en communications mobiles a hauts debits peuvent s'avérer extrêmement difficiles a estimer précisément. Nous proposons dans cet mémoire de thèse deux méthodes d'estimation de canal très sélectif en temps et en fréquence bases sur le critère du Maximum a Posteriori traitant le signal reçu par blocs. Ces algorithmes reposent sur un modèle de canal obtenu suivant la decomposition orthogonale de la matrice d'auto corrélation du canal selon le théorème de decomposition orthogonale de Karhunen¬Loève. Nous présenterons également les performances de ces nouvelles techniques comparées a celles de méthodes classiques d'estimation de canal ainsi que la robustesse de ces techniques a l'erreur d'estimation des statistiques du canal.