Research On Portfolio Selection With Probability Criterion And Fuzzy Criterion

Stochastic and fuzzy are two main aspects of the uncertainty in the financialmarket. The uncertainty of securities' return rate is the case. In this thesis, the modelsof portfolio selection with probability criterion and fuzzy criterion are put forwardrespectively and their hybrid intelligent algorithms are also designed. The concretecontents are as follows:An investor may have a claim for the expected rate of return, and hope to find aset of securities to maximize the probability of his achievement. So the models ofportfolio selection with probability criterion are put forward. The criterion function isthe probability that the return rate of the portfolio is not lower than a given expectedrate. For dynamic portfolio selection, it is the sum of probability that the return rate ofportfolio at the end of each period is not lower than a given one or the probability thatthe terminal return rate of portfolio is not lower than a given one.The financial market is characterized by fuzziness because of an investor'ssubjective judgment. Therefore, the models of portfolio selection with fuzzy criterionare investigated. The criterion function is the possibility (necessity or credibility) thatthe return rate of portfolio is not lower than a given expected rate. For dynamicportfolio selection, it is the sum of possibility (necessity or credibility) that the returnrate of portfolio at the end of each period is not lower than a given one or thepossibility (necessity or credibility) that the terminal return rate of portfolio is notlower than a given one.The models of portfolio selection with probability criterion and fuzzy criterionare no longer solved by the traditional methods since the criterion functions can't beconverted to their deterministic equivalents and crisp equivalents. Hybrid intelligentalgorithms are designed when stochastic simulation (fuzzy simulation) based geneticalgorithms and artificial neural network are integrated. The criterion functions arecalculated by stochastic simulation (fuzzy simulation) and optimized by geneticalgorithms. During dynamic portfolio selection, the approximate functions of thestrategy and criterion function can be obtained by using artificial neural network tosubstitute for their numerical solutions in the preceding step. Illustrate examples aregiven and the effectiveness of the proposed hybrid intelligent algorithms is shown.