Stock markets are very important in modern societies and their behaviour have serious implications in a wide spectrum of the world’s population. Investors, governing bodies and the society as a whole could benefit from better understanding of the behavior of stock markets. The traditional approach to analyze such systems is the use of analytical models. However, the complexity of financial markets represents a big challenge to the analytical approach. Most analytical models make simplifying assumptions, such as perfect rationality and homogeneous investors, which threaten the validity of analytical results. This motivates alternative methods. In this work, we developed an artificial financial market and used it to study the behavior of stock markets. In this market, we model technical, fundamental and noise traders. The technical traders are sophisticated genetic programming based agents that co-evolve (by means of their fitness function) by predicting investment opportunities in the market using technical analysis as the main tool. With this endogenous artificial market, we identified conditions under which the statistical properties of price series in the artificial market resembles those of the real financial markets. Additionally, we modeled the pressure to beat the market by a behavioral constraint imposed on the agents reflecting the Red Queen principle in evolution. We have demonstrated how evolutionary computation could play a key role in studying stock markets.

Abstract. In recent years the computers have shown to be a powerful tool in financial forecasting. Many machine learning techniques have been utilized to predict movements in financial markets. Machine learning classifiers involve extending the past experiences into the future. However the rareness of some events makes difficult to create a model that detect them. For example bubbles burst and crashes are rare cases, however their detection is crucial since they have a significant impact on the investment. One of the main problems for any machine learning classifier is to deal with unbalanced classes. Specifically Genetic Programming has limitation to deal with unbalanced environments. In a previous work we described the Repository Method, it is a technique that analyses decision trees produced by Genetic Programming to discover classification rules. The aim of that work was to forecast future opportunities in financial stock markets on situations where positive instances are rare. The objective is to extract and collect different rules that classify the positive cases. It lets model the rare instances in different ways, increasing the possibility of identifying similar cases in the future. The objective of the present work is to find out the factors that work in favour of Repository Method, for that purpose a series of experiments was performed. 1

Abstract. The aim of this work is to forecast future events in financial data sets, in particular, we focus our attention on situations where positive instances are rare, which falls into the domain of Chance Discovery. Machine learning classifiers extend the past experiences into the future. However the imbalance between positive and negative cases poses a serious challenge to machine learning techniques. Because it favours negative classifications, which has a high chance of being correct due to the nature of the data. Genetic Algorithms have the ability to create multiple solutions for a single problem. To exploit this feature we propose to analyse the decision trees created by Genetic Programming. The objective is to extract and collect different rules that classify the positive cases. It lets model the rare cases in different ways, increasing the possibility of identifying similar cases in the future. The over-learning produced by this method attempts to compensate the lack of positive cases. To illustrate our approach, it was applied to a data set composed by closing prices from the London Financial Market for finding investment opportunities with very high returns. From experiment results we showed that the Repository Method can consistently improve both the recall and the precision. Keywords: Chance Discovery, Classification, Genetic Programming. 1

presented to discover patterns in financial data sets to detect investment opportunities. ECR is designed to classify in extreme imbalanced environments. This is particularly useful in financial forecasting given that very often the number of profitable chances is scarce. The proposed approach offers a range of solutions to suit the investor’s risk guidelines and so, the user could choose the best trade-off between miss-classification and false alarm costs according to the investor’s requirements. Receiver Operating Characteristics (ROC) curve and the Area Under the ROC (AUC) have been used to measure the performance of ECR. Following from this analysis, the results obtained by our approach have been compared with those one found by standard Genetic Programming (GP), EDDIE-ARB and C.5, which show that our approach can be effectively used in data sets with rare positive instances. Key words: Evolving comprehensible rules, machine learning, evolutionary algorithms. 1

Abstract — This work is motivated by financial forecasting using Genetic Programming. This paper presents a method to post-process decision trees. The processing procedure is based on the analysis and evaluation of the components of each tree, followed by pruning. The idea behind this approach is to identify and eliminate rules that cause misclassification. As a result we expect to keep and generate rules that enhance the classification. This method was tested on decision trees generated by a genetic program whose aim was to discover classification rules in financial stock markets. From experimental results we can conclude that our method is able to improve the accuracy and precision of the classification. I.

Forecasting is an important activity in finance. Traditionally, forecasting has been done with in-depth knowledge in finance and the market. Advances in computational intelligence have created opportunities that were never there before. Computational finance techniques, machine learning in particular, can dramatically enhance our ability to forecast. They can help us to forecast ahead of our competitors and pick out scarce opportunities. This paper explains some of the opportunities offered by computational intelligence and some of the achievements so far. It also explains the underlying technologies and explores the research horizon. 1. Beating the market Wouldn’t it be nice if you can tell whether stock prices will go up or down tomorrow? Numerous attempts have been made to forecast stock prices. Motivation is not limited to financial gains. Financial stability could be improved should regulators be able to recognize patterns that signal market failure.

Abstract — This work is motivated by the interest in finding significant movements in financial stock prices. However, when the number of profitable opportunities is scarce the prediction of these cases is difficult. In a previous work, we have introduced Evolving Decision Rules (EDR) to detect financial opportunities. The objective of EDR is to classify the minority class (positive cases) in imbalanced environments. EDR provides a range of classifications in order to find the best balance between not making mistakes and not missing opportunities. The goals of this paper are: 1) to show that EDR produces a range of solutions to suit the investor’s preferences and 2) to analyze the factors that benefit the performance of EDR. A series of experiments was performed, EDR was tested using a data set from the London Financial Market. In order to analyse the EDR behaviour, another experiment was carried out using three artificial data sets, whose solutions have different level of complexity. Finally, an illustrative example was provided in order to show how a bigger collection of rules is able to classify more positive cases in imbalanced data sets. Experimental results show that: 1) EDR offers a range of solutions to fit the risk guidelines of different types of investors and 2) a bigger collection of rules is able to classify more positive cases in imbalanced environments. I.

Abstract—Financial forecasting is a lucrative and complicated application of machine learning. In this paper, we focus on the finding investment opportunities. We therefore explore four different Genetic Programming approaches and compare their performances on real-world data. We find that the novelties we introduced in some of these approaches indeed improve the results. However, we also show that the Genetic Programming process itself is still very inefficient and that further improvements are necessary if we want this application of GP to become successful. Keywords-Genetic programming; Decision rules; Classification;

method to suit different investment strategies

Constraints shield solutions from a problem solver. However, in the hands of trained constraint problem solvers, the same constraints that create the problems in the first place can also guide problem solvers to solutions. Constraint satisfaction is all about learning how to flow with the force of the constraints. Examples of using constraints to guide one’s search are abundant in complete search methods (e.g. see [1, 2]). Lookahead algorithms propagate constraints in order to (a) reduce the remaining problem to smaller problems and (b) detect dead-ends. Dependency-directed backtracking algorithms use constraints to identify potential culprits in dead-ends. This helps the search to avoid examining (in vain) combinations of variables assignments that do not matter. Constraint-directed search is used in stochastic search too. Constraints were used in Guided Local Search (GLS) [3] and Guided Genetic Algorithm (GGA) [4] to guide the search to promising areas of the search space. In stochastic methods, a constraint satisfaction problem is handled as an optimization problem, where the goal is to minimize the number of constraints violated. The approach in