The Studying On The Models And Optimal Methods Of The Computable Portfolio Selection

The mean-variance portfolio selection model proposed originally by Markowitz in 1952, has played an important role in the development of modern portfolio selection theory. It has pushed the mathematic finance and finance engineering forward.Usually, investors have an aversion to risk and pursue maximum return. The optimal portfolio should be an efficient portfolio with maximum utility. The investors used computing technology and optimal methods studying portfolio selection.The present dissertation, based on pivoting algorithms, makes a deep and systematic investigation on some new models of portfolio theory from constraint of subjection, expected utility and different calculating risk. The main researches and creative results of this dissertation are shown as follows:1. The paper studied five kinds of portfolio selection models considering not short sale, with the upper and lower bound constraint, total volume of trade constraint, cash deposit constraint and mortgage constraint, and used pivoting algorithms solving the models. The model considering not short sale has three kinds which are only with risk asset, with free-risk asset that lending and borrowing rates are same, and with free-risk asset that lending and borrowing rates are different. At last, the paper indicates that free risk can increase investment opportunity and different trade constraints have different efficient portfolio selection.2. Considering not short sale and under constraint of VaR, the paper proposed three different portfolio selection models and uses pivoting algorithms and the sequence of quadratic programming method solving the models. At last, the paper gets the result that considering the constraint of VaR can decrease the risk.3. Considering the transaction costs, the paper studied sever convex and concave cost mean-variance models and uses the pivoting algorithms and branch bound algorithm solving the models. At last, the paper gets the result that the optimal solutions of the four models are different. So the investors should consider the transaction costs.4. Considering the short sale and not short sale, the paper proposes three different expected utility portfolio selection models. The models with short sale are solved by Lagrange method. The paper uses pivoting algorithms solving the three mean-variance models without short sale. At last, the paper gets the result that the efficient frontiers of the mean-variance portfolio selection model and expected utility portfolio selection model are same.5. Except variance, there are several kinds of methods measuring the risk of portfolio. The paper studies five kinds of portfolio models that are mean-VaR, mean below semi-variance, mean-absolute deviation, mean semi-absolute deviation and mean- average absolute deviation. The author uses different algorithms solving the models.At last, the models of mean-variance, mean-VaR, mean semi-absolute deviation and mean- average absolute deviation and algorithms were proved efficient by two examples of Shaihai security market and American security market.