Solving Portfolio Investment Model With Full Transaction Cost Based On Hybrid Genetic Algorithm

The portfolio investment model proposed by Markowitz, who was the founder of this theory, has been paid extensive attentions during the last decades. However, this theory is established on a series of strict assumptions, such as no friction in finance market or dividing stocks freely. So the effectiveness and application of this model are decoupled greatly in actual transactions. Recently, scholars inland or abroad have carried on so thorough a research on it and brought forward a few modifications or improvements, for instance, joining in the transaction cost and the requirement of no dividing stocks. But considering the complexity of solving this model, many people usually simplify the transaction cost. So it often induces to an unfaithful result and can not provide enough reference for investors. Consequently, in this paper we present a more actual portfolio investment model, which is based on all requirements of the actual finical market such as no dividing stocks and all kinds of fees. This model makes up for the shortage of the former ones, which always simplify the transaction cost. And it is closer to the facts of domestic finance market.Secondly, most scholars take on the original genetic algorithm as main means to solve the investment model. As a kind of global searching method for the complex optimization problems, genetic algorithm has the characters of simpleness and fast convergence. But there are also some defaults when using GA in actual applications, such as earliness and poor local searching ability. So a more robust method is our favorite when solving the model. From the former research, we can know that some popular algorithms, for example, the steepest gradient, the mountain-climbing and the simulated annealing method, all have better local searching ability. So in this paper a hybrid SAGA combined with dynamic penalty function algorithm is used to solve the model founded before. To enhance the effectiveness of the GA algorithm, the SA method is used not only to select penalty function but also to improve the penalty coefficients. Finally, the algorithm is validated by an investment example. And the experiment results indicate that our algorithm has better searching ability and can avoid the occurring of earliness effectively. Compared with the traditional GA algorithms, our method converges faster and has better solving precision. To investors, it's a better tool for decision-making.