Credibilistic portfolio optimization. Individual investors perspective

The fundamental goal of every financial investment is to maximize profit. A sharp increase of turnover in the financial markets led to the rapid development of studies in the field of investment portfolio optimization. These studies focus mainly on measuring the risk associated with an investment, and the maximization of profits. Nowadays, individual investors are overwhelmed with investment options as well as a continuous flow of data. For this reason we will focus in this publication on the perspective of individual investors. As experiments have shown, investors do not strictly adhere to the principles presented in normative market models. In economic practice, the data available to a decision maker is often random, inaccurate, and often expressed in approximate or even linguistic form. This book synthesizes elements of fuzzy variable theory in the light of Liu's credibility theory for the needs of portfolio analysis.

Introduction
1. Rate of return versus uncertainty of capital investments
Introduction
1.1. Classification of uncertainty
1.1.1. The concept of risk and uncertainty
1.1.2. Uncertainty classifications
1.2. Implementation of uncertainty and risk in investment assessment
1.2.1. Random approach
1.2.2. Fuzzy approach
1.2.3. Approach based on possibility theory
1.2.4. Approach based on credibility theory
1.2.5. Fuzzy-random approach
Summary
2. Individual investor profile
2.1. Polish statistical investors
2.2. Survey Stock Portfolio Selection – criteria and investor preferences
2.2.1. Methodology
2.2.2. Results
Summary – evaluation of optimization task usefulness
3. Th e concept of a fuzzy rate of return
3.1. Fuzzy measures
3.2. Th e concept of a fuzzy variable
3.2.1. Distribution of credibility
3.2.2. The fuzzy variable membership function
3.3. Fuzzy rate of return
3.3.1. Expected value
3.3.2. Uncertainty measures
4. Method for determining a fuzzy rate of return
4.1. Expert approach
4.2. Statistical approach
4.2.1. Interpolation of a continuous membership function
4.3. Empirical study
4.3.1. Methodology and data
4.3.2. Results
5. Stock portfolio optimization problems
5.1. Portfolio selection problems using uncertainty and profi t measures
5.1.1. Portfolio selection problems using dispersion measures
5.1.2. Entropy measures
5.1.3. Models based on credibility measures and safety criteria
Summary
5.2. Models using measures of attitude towards uncertainty and investor preferences
5.2.1. Mean-risk model
5.2.2. Regret minimization model
5.2.3. Investor satisfaction maximization model
Summary
5.3. Empirical study
5.3.1. Methodology and data
5.3.2. Synthetic measure of optimization model evaluation
5.3.3. Results
Summary
Appendix
Appendix A. Survey of stock portfolio selection – criteria and investor preferences
Appendix B. Survey – results
References
Index