Abstract: An optimal portfolio selection problem based on the expected utility maximization and nonparametric estimation framework is investigated in this paper. Unlike most studies in which the assets' returns are supposed to obey some special distribution forms, any assumption about the distributions of the asset returns are not required in this paper. Firstly in case of general utility function, using the nonparametric estimation of the portfolio return's density function, the basis nonparametric calculated formula for expected utility is given, and the basic framework for expected utility maximization portfolio selection problem is established. Then, under the assumption that investors hold the power utility function, the specific nonparametric estimated formula for expected utility is obtained, and the specific numerical algorithms for the optimal investment strategy of the utility maximization model is proposed. Finally, a numerical example based on real daily return data of 11 stocks from Chinese stock market is given to illustrate the usefulness and effectiveness of our results. The nonparametric estimation framework introduced in this paper is general and adaptive. It can be used to investigate the portfolio selection model under various realistic conditions, such as inequality constraints and transaction costs.

Key words: portfolio selection, power utility function, expected utility maximization model, nonparametric estimation, optimal investment strategy