Discussion On Portfolio Management Problems With Probability Criterion

The modern financial theory provided a scientific method for the portfolio investment. Securities investment is one of the finance investments in high risk, so the evaluation and measure of the risk in investing process became the sticking point, and the research of risk measurement is the hotspot in finance invest research at all times. Markowitz mean-variance model inaugurate a new period for quantify of portfolio investment risk. However, as the research going deeply, it is found that the mean-variance model not only has flaw in theory, but also disagreeing with the real security business. Firstly, as indicated by lots of data from security business, yields vector is not always in Normal Distribution. Secondly, in Markowitz mean-variance model, win and loss are all regard as the same, which disobey the investor's real feeling for risk.For repairing the drawback of Markowitz mean-variance model, people have advanced a lot of other investment risk measurement theory and estimating method. There are many other models have been advanced from Markowitz's portfolio model. However, every kind of model has its localization, so in this thesis, a new kind of portfolio investment model with probability criterion is investigated. In this paper, several combinations of common investment decision model shortcomings, the theory of probability theory and portfolio investment combined, give a class of perfect combination of criteria based on probabilistic model of investment decision. The paper made a comprehensive model of the probability criterion detailed analysis, emphasizing the practical value of the model.Probabilistic model of such guidelines into the traditional methods used to solve the nonlinear programming model,so that it can be solved by computer.Allow short selling in the market conditions, considering transaction costs, the hands of investors have already established a number of securities held by the probability criterion, the optimal solution satisfies the necessary conditions, and proves existence and uniqueness of optimal solutions, the objective function of the model range was estimated, the optimal solution was derived. Finally, an example of the model simulation with satisfactory results.