Using fuzzy goal approach for portfolio optimizition

Abstract

Mathematical applications is widely used in di erent aspects of human life, particularly in nance. Quantitative models are created to nd the optimal solutions for nancial problems have helped signi cantly banking system, fund management, and brokerage companies. A common example is that the forming of portfolio which could satisfy conditions from investors is really necessary, particularly in the modern world where people is easy to be a ected by incorrect informations. In the past, the Modern Portfolio Theory of Markowitz had been mentioned many times. This is considered as a rm base for lots of nancial model in later century. However, the growth of human demand requires a model which can solve many di erent conditions in the same time. There are many ways to solve the above issues. As far as I concerned, Preemptive Fuzzy Goal Programming is the best method which can be used to the nd optimal investment ratio. Furthermore, the usage of fuzzy numbers supports investor's selection become more exible than ordinary number. This research will focus on using Preemptive Fuzzy Goal Approach for portfolio optimization. The proposed method has been tested with data from Vietnam Stock Market - the adjusted closing price of 30 stocks traded in VN30 Equal Weight Index in downward and upward period of the market. The result is compared with those from Markowitz's model. It shows that the Preemptive Fuzzy Goal Programing perform better than Markowitz in both upward and downward trend of Vietnam stock market. Due to the scope of Vietnamese legal, running the research model had to face many problems without making assumptions. In the near future, this research will be improved to be suitable to Vietnam stock market regulations. Keywords: Application of Mathematics, Portfolio Optimization, Markwotiz's model, Preemptive Fuzzy Goal Programming.