This paper provides a survey of credibility theory that is a new branch of mathematics for studying the behavior of fuzzy phenomena. Some basic concepts and fundamental theorems are introduced, including credibility measure, fuzzy variable, membership function, credibility distribution, expected value, variance, critical value, entropy, distance, credibility subadditivity theorem, credibility extension theorem, credibility semicontinuity law, product credibility theorem, and credibility inversion theorem. Recent developments and applications of credibility theory are summarized. A new idea on chance space and hybrid variable is also documented.

A survey of credibility theory

Nowadays, many current real financial applications have nonlinear and uncertain behaviors which change across the time. Therefore, the need to solve highly nonlinear, time variant problems has been growing rapidly. These problems along with other problems of traditional models caused growing interest in artificial intelligent techniques. In this paper, comparative research review of three famous artificial intelligence techniques, i.e., artificial neural networks, expert systems and hybrid intelligence systems, in financial market has been done. A financial market also has been categorized on three domains: credit evaluation, portfolio management and financial prediction and planning. For each technique, most famous and especially recent researches have been discussed in comparative aspect. Results show that accuracy of these artificial intelligent methods is superior to that of traditional statistical methods in dealing with financial problems, especially regarding nonlinear patterns. However, this outperformance is not absolute.

A comparative survey of artificial intelligence applications in finance: artificial neural networks, expert system and hybrid intelligent systems

Mean-variance-skewness model for portfolio selection with fuzzy returns

The coinciding development of multiobjective evolutionary algorithms (MOEAs) and the emergence of complex problem formulation in the finance and economics areas has led to a mutual interest from both research communities. Since the 1990s, an increasing number of works have thus proposed the application of MOEAs to solve complex financial and economic problems, involving multiple objectives. This paper provides a survey on the state-of-the-art of research, reported in the specialized literature to date, related to this framework. The taxonomy chosen here makes a distinction between the (widely covered) portfolio optimization problem and the other applications in the field. In addition, potential paths for future research within this area are identified.

A Survey on Multiobjective Evolutionary Algorithms for the Solution of the Portfolio Optimization Problem and Other Finance and Economics Applications

Making R&D portfolio decision is difficult, because long lead times of R&D and market and technology dynamics lead to unavailable and unreliable collected data for portfolio management. The objective of this research is to develop a fuzzy R&D portfolio selection model to hedge against the R&D uncertainty. Fuzzy set theory is applied to model uncertain and flexible project information. Since traditional project valuation methods often underestimate the risky project, a fuzzy compound-options model is used to evaluate the value of each R&D project. The R&D portfolio selection problem is formulated as a fuzzy zero-one integer programming model that can handle both uncertain and flexible parameters to determine the optimal project portfolio. A new transformation method based on qualitative possibility theory is developed to convert the fuzzy portfolio selection model into a crisp mathematical model from the risk-averse perspective. The transformed model can be solved by an optimization technique. An example is used to illustrate the proposed approach. We conclude that the proposed approach can assist decision makers in selecting suitable R&D portfolios, while there is a lack of reliable project information.

(OMEGA- International Journal of Management Science, 35(3):247-257)A fuzzy set approach for R&D portfolio selection using a real options valuation model

Mean-semivariance models for fuzzy portfolio selection

Fuzzy chance-constrained portfolio selection

Two new models for portfolio selection with stochastic returns taking fuzzy information

This short paper proposes two types of credibility-based fuzzy mean-entropy models. In the short paper, entropy is used as the measure of risk. The smaller the entropy value is, the less uncertainty the portfolio return contains, and thus, the safer the portfolio is. Furthermore, as a measure of risk, entropy is free from reliance on symmetrical distributions of security returns and can be computed from nonmetric data. In addition, the short paper compares the fuzzy mean-variance model with the fuzzy mean-entropy model in two special cases and presents a hybrid intelligent algorithm for solving the proposed models in general cases. To illustrate the effectiveness of the proposed algorithm, the short paper also provides two numerical examples.

Xiaoxia Huang

Papers

Mean-semivariance models for fuzzy portfolio selection

Fuzzy chance-constrained portfolio selection

Two new models for portfolio selection with stochastic returns taking fuzzy information

Mean-Entropy Models for Fuzzy Portfolio Selection

Optimal project selection with random fuzzy parameters