| The mean-variance methodology for the portfolio selection problem, posed originally by Markowitz in 1952, has played an important role in the development of modern portfolio selection theory. It combines probability and optimization techniques to model the behavior of investment under uncertainty. Usually, investors have an aversion to risk and pursue maximum utility; the optimal portfolio should be an efficient portfolio with maximum utility. Clearly, the efficient portfolio selection problem is a very important topic for modern portfolio theory.A Genetic Algorithm is a probabilistic, inherent parallel search approach, inspired by evolutionary mechanisms, natural selection and genetics. A GA starts with a population of randomly generated solutions called candidates to explore the solution space of a problem. The population of solutions is modified to a new population by applying three operators similar to natural genetic operators, reproduction, crossover, and mutation. A GA works iteratively by successively applying these three operators in each generation till a termination criterion is satisfied. Nowadays, the Genetic Algorithm technique has been successfully applied to a wide variety of problems, because it is simple and robust, especially easy to implement.The main work of the paper is establishing static and dynamic the model for portfolio investment in the condition of considering friction factors in market. Then, propose a reliable and efficient genetic algorithm to solve the static and dynamic the model for portfolio investment. In Chapter 1,we briefly introduce the research status and meaning of modern portfolio theory and the Genetic Algorithm. In Chapter 2, we give a brief introduction to the basic conception and theories of the Genetic Algorithm. In Chapter 3, we elaborate on Markowitz's portfolio model, and put forward double objective static and dynamic the model for portfolio investment under the attrition market. In Chapter 4,we design a genetic algorithm that can solve static and dynamic portfolio model. And the empirical analysis shows that the model is rational and the algorithm is effective. |
