A fuzzy decision maker for portfolio problems

In this paper, we investigate the decision making problem which maximizes a cost function for a system with unknown dynamics. Only implicit message coming from future trend of the system can be obtained. After set up the framework of such an optimization problem, we focus on how to determine an optimal sequence of portfolio adjustments, and the purpose is to maximize a utility function at the end of some periods. At the portfolio application, it is crucial to identify the future evolution of the portfolio composition. To this end, the well-known Black-Scholes pricing formula for option market is used to modify the parametric dynamic series. This is because the option market and the spot market are closely related and are affected by each other. Many implicit messages of stocks can be obtained through examining their options. From the implied volatility and the open interest, the investors´ viewpoints on the stock prices in the future can be extracted. Then, it can improve the conventional Markowitz portfolio to establish a one-period and a multi-period fuzzy decision maker. These efficient decision makers lie on the more reliable dynamic series of the portfolio composition, and can avoid overestimating and/or underestimating expected return and expected risk. Numerical case study on many scenarios also shows the proposed decision-making scheme exhibits the highest profit for asset allocation among several portfolio models.