Abstract
Vast pools of historical financial information are available on economies, industry, and individual companies that affect investors’ selection of appropriate portfolios. Fuzzy data provides a good tool to reflect investors’ opinions based on this information. A possibilistic mean variance safety-first portfolio selection model is developed to support investors’ decision making, to take into consideration this fuzzy information. The possibilistic-programming problem can be transformed into a linear optimal problem with an additional quadratic constraint using possibilistic theory. We propose a cutting plane algorithm to solve the programming problem. A numerical example is given to illustrate our approach.
Highlights
Portfolio selection regards asset selection which maximizes an investor’s return and minimizes her risk
The mean safety-first approach only controls the downside risk of security return. Another limitation of both approaches is that the underlying distribution of the rate of return is not well understood, and there are no higher degree information is utilized except means, covariances, so we propose the following mean variance safety-first portfolio selection model: (MVSF )
Variance and co-variance are derived directly from fuzzy numbers, which is different from the probability theory where variance and co-variance are derived from a great deal of historical data such as Markowitz’s mean variance framework and the safety-first portfolio model
Summary
Portfolio selection regards asset selection which maximizes an investor’s return and minimizes her risk. Watada(2001) presented another type of portfolio selection model based on the fuzzy decision principle This model is directly related to the mean-variance model, where the goal rate for an expected return and the corresponding risk are described by logistic membership functions. Fuzzy variance and covariance are derived directly from fuzzy numbers, which are different from the probability theory where variance and covariance are derived from a great deal of historical data such as Markowitz’s mean variance framework and the safety-first portfolio model. This will, on the one hand, reduce the computation complexity and on the other hand, overcome the hurdle of semi-positive covariance matrix as required in a great deal of portfolio models based on the probability theory.
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