Multi-objective Optimization Model Portfolio Under Fuzzy Environment

Financial market uncertainties are mainly divided into random uncertainties and fuzzy uncertainties, the subjective judgment of the stock market and investors often show the fuzzy uncertainties. At present the typical model portfolio is mostly through the method of probability theory and focus on the basis of random uncertainties to study.This article is based on analyzing and summarizing the past securities portfolio theory, building the portfolio multi-objective optimization model in a fuzzy environment with the multi-objective programming model. This model is allowing short buying and short selling the securities, which means the margin trading. This paper established three goals: revenue maximization, risk minimization and gaining the maximization of the partial degrees. Then we use these three goals for their membership function fuzzed.The key of the model is the fuzziness, which is a very difficult thing to make a correct investment portfolio decision based on the fuzziness. This article is through the multi-objective fuzzy membership function to establish a multi-objective programming model. In order to facilitate calculation easily and find out the actual portfolio, this article will make fuzzy multi-objective programming problem for reduction processing.In this paper, we divide the portfolio into the risk-free asset portfolio and not being risk-free asset portfolio to study and discuss the portfolio model, and contact actually formulated exist risk-free asset portfolio more close to reality.Through the research and analysis in this paper, we can find a more reasonable portfolio decision for investors, allowing investors to increase profitability and reduce risk as far as possible, providing the fund managers a increasing liquidity and capital safety approach, providing a good investment platform for the whole market environment.