An automatic trading system for fuzzy portfolio optimization problem with sell orders

This paper deals with a portfolio optimization problem with sell orders, in which the investor will immediately sell the risky assets once their prices reach the preset sell thresholds. Departing from the traditional portfolio models, the investor needs to determine not only an investment proportion but also a sell threshold for each risky asset. We formulate the portfolio problem as a sequential decision problem and propose an automatic trading system with three stages to determine the investment strategy at the beginning of each period. In Stage 1, we formulate the return of an investment strategy as an LR-power fuzzy number based on the historical data and propose a fuzzy mean–semi-variance portfolio optimization model with sell orders. In Stage 2, we design a multi-objective genetic algorithm to solve the proposed model. In Stage 3, we select an optimal investment strategy among the efficient solutions based on the fuzzy Value-at-Risk ratio. Moreover, we conduct two case studies in the real stock market to illustrate the effectiveness and practicability of the proposed model and algorithm. The comparison results show that the proposed trading system has a better out-of-sample performance than the other ones.