| Financial market is a large system in economic system, and its healthy development is closely related to the sustainable development of a country's economy. Securities investment is an important part of the financial market, and it is very significant to evaluate portfolios reasonably and accurately, which can not only choose high-quality products with great guide for investors, but also improve survival of the fittest and the healthy development of capital market. However, it's difficult to estimate the expectation and covariance matrix of asset return accurately and the benefits as well as risks of securities are uncertain because of the complexity of the real investment environment, which makes investors make investment decision in an uncertain environment.Under the circumstance of uncertain parameters, the paper try to provide the definition of portfolio performance based on the true frontier and then construct the corresponding nonlinear efficiency evaluation model. However, it's not convenient to obtain the analytical solution of frontier and the nonlinear model is difficult to solve. Providing the assumption that the real frontier is a concave function, we use DEA frontier to approximate the real frontier and then estimate the efficiency of portfolio. Considering that there are many restrictions and market frictions in the actual financial market, we consider transaction costs as well as volume restriction and further study portfolio efficiency evaluation with market frictions under the circumstances of uncertain parameters.In the simulation analysis, we use the definition (based on the true frontier) and the DEA model (based on DEA efficient frontier) to evaluate the efficiency of portfolio under the circumstance of uncertain parameters. The results show that we can get reliable efficiency evaluation results in the case of small samples, which illustrates the effectiveness and feasibility of the proposed DEA model. |
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