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

Portfolio selection is concerned with selecting an optimal portfolio that can strike a balance between maximizing the return and minimizing the risk among a large number of securities. Traditionally, security returns were regarded as random variables. However, there are cases that the predictions of security returns are given mainly based on experts' judgements and estimations rather than historical data. In this paper, we introduce a new type of variable to reflect the subjective estimations of the security returns. A risk index for uncertain portfolio selection is proposed and a new safe criterion for judging the portfolio investment is introduced. Based on the proposed risk index, a new mean-risk index model is developed and its crisp forms are given. In addition, to illustrate the application of the model, two numerical examples are also presented.

A risk index model for portfolio selection with returns subject to experts' estimations

A portfolio is a combination of a number of securities. Portfolio analysis is a quantitative method for selecting an optimal portfolio that can strike a balance between maximizing the return and minimizing the risk in various uncertain environments. To select the optimal portfolio, we must first answer the questions “what is return of a portfolio” and “what is risk of the portfolio”. If we could only use the natural language like “the likely gain of the portfolio” to describe return and “the likely loss of the portfolio” to describe risk, we would not be able to quantify return and risk of the portfolio. Then it would be impossible to compare the return level and risk level of portfolios, let alone find the maximum return and minimum risk. To use measurable terms to define return and risk, we should start with input data, i.e., the individual security returns.

Xiaoxia Huang

Papers

A risk index model for portfolio selection with returns subject to experts' estimations

What Is Portfolio Analysis

Risk index based models for portfolio adjusting problem with returns subject to experts' evaluations

Project selection and scheduling with uncertain net income and investment cost

Mean-variance model for fuzzy capital budgeting