Credibilistic Portfolio Selection

Abstract

Credibilistic portfolio selection deals with fuzzy portfolio selection by means of credibility theory. Fuzzy portfolio selection problem was researched from 1990s. Early researchers employed possibility as the basic measure of the occurrence of a fuzzy event and most of them devoted themselves to extending Markowitz’s mean-variance selection idea. However, possibility measure is not self-dual. By using possibility, when the investors know the possibility level of a portfolio reaching a target return, they cannot know the possibility level of the opposite event, i.e., the event of this portfolio not being able to achieve the target return! This will confuse and worry the decision maker. Therefore, Huang proposed that we should use the self-dual credibility as the basic measure of the occurrence of a fuzzy event and study the fuzzy portfolio selection problems. To provide an instinct and observable information about loss amount and to accurately evaluate the loss degree, Huang [38] proposed that we should evaluate each likely loss level and the loss occurrence chance instead of just focusing on the average information of loss. Looking at loss from a panoramic perspective, Huang provided a general definition of risk, i.e., the risk curve, and proposed a mean-risk model based on this new definition. In addition, Huang proposed a spectrum of simplified versions of the risk and proposed a system of credibilistic portfolio selection models [41] including mean-risk model [38], β-return-risk model [27], credibility minimization model, mean-variance model [33], mean-semivariance model [37], and entropy optimization model [39].

This chapter will first introduce some necessary knowledge about credibility theory. The reason for adopting credibility measure rather than possibility measure is given. Then we will introduce the definitions of risk and the credibilistic portfolio selection models. Crisp equivalents of the fuzzy models in some special cases will also be presented. After that, we will provide a general solution algorithm for solving the credibilistic portfolio selection models.