Research On Portfolio Selection Models And Heristic Algorithms

Based on stochastic theory and fuzzy possiblistic theory we study some portfolio selection problems, and we use two kinds of heuristics algorithms-genetic algorithm and particle swarm optimization for our proposed problems.The primary contents will be generalized as follows:1. Considering the practicality of moder portfolio selection theory, we propose a constrained portfolio selection model based on the no short sale, transaction costs and minimum lot constraints. Due to these complex constraints our proposed problem becomes a mixed integer optimization problem and traditional algorithms can't solve it efficiently. Thus, an improved genetic algorithm is designed to solve our proposed problem.2. Based on the risk measurement of mean-absolute deviation we study three kinds of portfolio selection models with transaction costs, namely, mean-absolute deviation model with transaction costs, mean-semiabsolute deviation model with transaction costs, and mean-maxmin-semiabsolute deviation model with transaction costs, then an example of portfolio problem is given to compare three kinds of models, and comparative analysis is also given to show that transaction costs has great impact on the portfolio selection.3. The admissible efficient portfolio model with transaction costs and quantity constrains are studied under the assumption that the expected return and risk of assets have admissible errors. Firstly, the admissible efficient portfolio model with transaction costs and quantity constrains is proposed. Secondly, traditional optimization algorithms fail to work efficiently for our proposed problem, so we designed an improved particle swarm optimization algorithm to solve it. At last, the effectiveness of the improved particle swarm optimization algorithm is demonstrated on a realistic portfolio selection problem.4. Some fuzzy possibilistic portfolio selection problems are studied based on the possibilistic theory under the assumption that the returns of assets are fuzzy numbers. Firstly, we propose a new conception of possiblistic mean, namely, weighted possibilistic mean, which is the extension definition proposed by Carlsson and Fuller, then the possiblistic portfolio selection model with utility function is proposed. Secondly, based on the theory of possiblistic theory the possbilistic portfolio selection model with transaction costs is proposed, then the method for solving this problem is given. At last, the portfolio selection problem with borrowing constraints, and with multiple constraints (borrowing, liquditity and investing quantity constraints) are studied, respectively.5. Study some possiblistic portfolio selection problems under returns of assets are some special fuzzy number. Regarding returns of assets as triangle fuzzy numbers, trapezoidal fuzzy numbers and normal fuzzy numbers respectively, some possiblistic portfolio selection models are proposed based on two kinds of definition of possiblistic mean and variance. Then, some comparative analyses are given to show the difference of these models under different definition.