An Approach for a Multi-Period Portfolio Selection Problem by considering Transaction Costs and Prediction on the Stock Market

This paper addresses a method to solve multi-period portfolio selection on the stock market. The problem seeks an investor trade stocks with finite budget and given integer number of hold in portfolio. must be performed through stockbroker that charges its respective transaction cost has minimum required amount. A mathematical model been proposed deal constrained problem. objective function is find best risk-return rate; thus, Sharpe Ratio Treynor are used as functions. returns same for these ratios, but risks not considering covariance systematical risk. predicted using Neural Net Long-Short-Term Memory (LSTM). neural net compared simple forecasting methods Mean Absolute Percentage Error (MAPE). Computational experiments show quality prediction by LSTM. heteroskedastic risk estimated Generalized Autoregressive Conditional Heteroskedasticity (GARCH), adjusting variance every period; this measure Ratio. experiment contemplates weekly 5 10 122 periods each Chilean market ratio. ten stocks, performing 62.28% real return beating market, represented Selective Stock Price Index (IPSA). Even worst portfolio, Ratio, overcomes IPSA cumulative yield stocks.