Abstract: This paper presents a remarkable model for portfolio selection using inverse-variance weighting and machine learning techniques such as hierarchical clustering algorithms. This method allows building diversified portfolios that have a good balance sector exposure and style exposure, respect to momentum, size, value, short-term reversal, and volatility. Furthermore, we compare performance for seven hierarchical algorithms: Single, Complete, Average, Weighted, Centroid, Median and Ward Linkages. Results show that the Average Linkage algorithm has the best Cophenetic Correlation Coefficient. The proposed method using the best linkage criteria is tested against real data over a two-year dataset of one-minute American stocks returns. The portfolio selection model achieves a good financial return and an outstanding result in the annual volatility of 3.2%. The results suggest good behavior in performance indicators with a Sharpe ratio of 0.89, an Omega ratio of 1.16, a Sortino ratio of 1.29 and a beta to S&P of 0.26.

Abstract: In the present work, the European style fixed strike Asian call option with arithmetic and continuous averaging is numerically evaluated where the volatility, the risk free interest rate and the dividend yield are functions of the time. A finite difference scheme consisting of second order HODIE scheme for spatial discretization and two-step backward differentiation formula for temporal discretization is applied. The scheme is proved to be second order accurate in space and time both. The numerical results are in accordance with analytical results.

Abstract: Portfolio optimization in stock markets has been investigated by many researchers. It looks for a subset of assets able to maintain a good trade-o control between risk and return. Several algorithms have been proposed to portfolio management. These algorithms use known return and correlation data to build subset of recommended assets. Dynamic stock correlation networks, whose vertices represent stocks and edges represent the correlation between them along the time, can also be used as input by these algorithms. This study proposes the denition of the constants of the classic mean-variance analysis using machine learning and weighted link prediction in stock networks (named as MLink). To assess the performance of MLink, experiments were performed using real data from the Brazilian Stock Exchange. In these experiments, MLink was compared with mean-variance analysis (MVA), a popular methods for portfolio optimization. According to the experimental results, the use of weighted link prediction in stock networks as input produced the best performance in the portfolio optimization task, resulting in a capital increase of 41% in 84 days.