The mean-variance portfolio selection based on the average and current profitability of the risky asset

Abstract: We study the continuous-time pre-commitment mean-variance portfolio selection in a time-varying financial market. By introducing two indexes which respectively express the average profitability of the risky asset (AP) and the current profitability of the risky asset (CP), the optimal portfolio selection is represented by AP and CP. Furthermore, instead of the traditional maximum likelihood estimation (MLE) of return rate and volatility of the risky asset, we estimate AP and CP with the second-order variation of an auxiliary wealth process. We prove that the estimations of AP and CP in this paper are more accurate than that in MLE. And, the portfolio selection is implemented in various simulated and real financial markets. Numerical studies confirm the superior performance of our portfolio selection with the estimation of AP and CP under various evaluation criteria.