The portfolio investment decisions about logarithmic utility

Logarithmic utility function is a kind of typical riskaverse utility function, in this paper, we will study the logarithmic utility function of the optimal portfolio problem. Use the method of Lagrange multiplier to solve the mean-variance efficient frontier, show the result in the r plane; base on the rule of efficient selection of portfolio, find this IDC and obtain optimal portfolio about the utility function; give examples to verify the results in the paper.