Fuzzy portfolio selection and its application to decision making

Rok, strany: 1997, 219 - 248

In this paper, the new methodologies of fuzzy portfolio selection and their applications to decision making are discussed. Especially, fuzzy mathematical programming based on a vague aspiration level given by a decision maker is examined. Portfolio selection has been originally proposed by H. M. Markowitz. The Markowitz's approach to the portfolio selection has difficulty to solve it. For instance, it is difficult to distinguish the portfolios on its efficient frontier, and an aspiration level and utility given by decision makers are not taken into consideration in the portfolio selection. In this paper, fuzzy portfolio selection is proposed to overcome the difficulty. The fuzzy portfolio selection enables us to obtain a solution which realizes the best within a vague aspiration level and a fuzzy goal given as a fuzzy number, which is obtained from the expertise of decision makers. In the conventional method to solve portfolio selections, the investing rate to each security is decided to realize the minimum risk under the constraint that the goal rate of an expected return given by a decision maker should be guaranteed. On the assumption that a decision maker has vague goal values for the expected return rate and the risk a-priori before solving the portfolio selection problem, we proposed the method in this paper to realize both vague goals employing a fuzzy concept to the treatment of the portfolio selection problem. As a result, the following remarks should be emphasized on the fuzzy portfolio selection. Some portfolio selection problem results in integer programming. A genetic algorithms, which is one of stochastic search algorithms, is employed to solve an integer programming. In this paper nonbinary string population is employed in the genetic algorithm instead of binary string population. The coding of nonbinary string population employed here is effective to reduce still births which do not fit to the environment, that is, reduce offspring which does not fit to the conditions of the problem. In order to confirm the effectiveness of this coding, we have applied the fuzzy mean-variance analysis to the fuzzy portfolio selection within the interval number of invested bonds and personnel allocation problem within the interval number of new employee. The results of these applications show effectiveness. Especially, in the latter personnel allocation problem it is shown that the unfitting individuals which are not appropriate to the problem are not produced. In the fuzzy portfolio selection problem we can propose the reallocation method of surplus fund which is obtained by the dealing constraints according to the satisfaction standard for the solutions. Mean-variance analysis which solves a portfolio selection problem will be applied to a resource allocation problem under the consideration of its risk. The application treated here is to solve a fuzzy portfolio selection within the restricted interval of the number of invested securities. These applications will show the effectiveness of the fuzzy mean-variance analysis.

ISO 690:

Watada, J. 1997. Fuzzy portfolio selection and its application to decision making. In Tatra Mountains Mathematical Publications, vol. 13, no.4, pp. 219-248. 1210-3195.

APA:

Watada, J. (1997). Fuzzy portfolio selection and its application to decision making. Tatra Mountains Mathematical Publications, 13(4), 219-248. 1210-3195.