The Open Fund's Optimal Portfolios

Following the operating mechanism of the open fund, we put forward some methods that solve the optimum investment combination problem of the open fund.Firstly, in terms of whether there are riskless assets and whether the ratio of surplus assets is fixed , we establish the mathematical model, single-period mean-variance model, for selecting optimal portfolios of the open fund, and derive the analytically expressions of optimal portfolios and the efficient frontiers for these models. We also discuss the relations and differences of these questions. Secondly, under the assumption that the risk assets are uncorrelated and there is no short-selling, we discuss the model of the open fund's portfolio, and offer the optimal solutions and efficient frontiers. At last, we set up the probability criterion model of the open fund, and give the proof of the existence of optimal solution.