Yong Fang & Kin Keung Lai 
Fuzzy Portfolio Optimization 
Theory and Methods

Most of the existing portfolio selection models are based on the probability theory. Though they often deal with the uncertainty via probabilistic – proaches, we have to mention that the probabilistic approaches only partly capture the reality. Some other techniques have also been applied to handle the uncertainty of the ?nancial markets, for instance, the fuzzy set theory [Zadeh (1965)]. In reality, many events with fuzziness are characterized by probabilistic approaches, although they are not random events. The fuzzy set theory has been widely used to solve many practical problems, including ?nancial risk management. By using fuzzy mathematical approaches, quan- tative analysis, qualitative analysis, the experts’ knowledge and the investors’ subjective opinions can be better integrated into a portfolio selection model. The contents of this book mainly comprise of the authors’ research results for fuzzy portfolio selection problems in recent years. In addition, in the book, the authors will also introduce some other important progress in the ?eld of fuzzy portfolio optimization. Some fundamental issues and problems of po- folioselectionhavebeenstudiedsystematicallyandextensivelybytheauthors to apply fuzzy systems theory and optimization methods. A new framework for investment analysis is presented in this book. A series of portfolio sel- tion models are given and some of them might be more e?cient for practical applications. Some application examples are given to illustrate these models by using real data from the Chinese securities markets.

Cuprins

Literature Review.- Survey for Portfolio Selection Under Fuzzy Uncertain Circumstances.- Portfolio Selection Models Based on Fuzzy Decision Making.- Fuzzy Decision Making and Maximization Decision Making.- Portfolio Selection Model with Fuzzy Liquidity Constraints.- Ramaswamy’s Model.- León-Liern-Vercher’s Model.- Fuzzy Semi-absolute Deviation Portfolio Rebalancing Model.- Fuzzy Mixed Projects and Securities Portfolio Selection Model.- Portfolio Selection Models with Interval Coefficients.- Linear Programming Model with Interval Coefficients.- Quadratic Programming Model with Interval Coefficients.- Portfolio Selection Models with Possibility Distribution.- Tanaka and Guo’s Model with Exponential Possibility Distributions.- Carlsson-Fullér-Majlender’s Trapezoidal Possibility Model.- Center Spread Model in Fractional Financial Market.- Fuzzy Passive Portfolio Selection Models.- Fuzzy Index Tracking Portfolio Selection Model.