Fang / Lai / Wang Fuzzy Portfolio Optimization

Theory and Methods
1. Auflage 2008
ISBN: 978-3-540-77926-1
Verlag: Springer Berlin Heidelberg
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, Band 609, 176 Seiten

Reihe: Lecture Notes in Economics and Mathematical Systems

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.

Autoren/Hrsg.

Fang, Yong

Lai, Kin Keung

Wang, Shouyang

Inhaltsverzeichnis

1;Preface;5
2;Contents;7
3;Part I Literature Review;11
3.1;1 Survey for Portfolio Selection Under Fuzzy Uncertain Circumstances;12
3.1.1;1.1 Introduction;12
3.1.2;1.2 Portfolio Selection Based on the Fuzzy Decision Theory;14
3.1.3;1.3 Portfolio Selection Based on Possibilistic Programming;16
3.1.4;1.4 Portfolio Selection Based on Interval Programming;22
4;Part II Portfolio Selection Models Based on Fuzzy Decision Making;26
4.1;2 Fuzzy Decision Making and Maximization Decision Making;28
4.2;3 Portfolio Selection Model with Fuzzy Liquidity Constraints;30
4.2.1;3.1 Introduction;30
4.2.2;3.2 Minimax Semi-absolute Deviation Risk Function;31
4.2.3;3.3 Fuzzy Liquidity of Securities;32
4.2.4;3.4 Model Formulation;34
4.2.5;3.5 Numerical Example;46
4.2.6;3.6 Conclusion;48
4.3;4 Ramaswamy’s Model;54
4.3.1;4.1 Introduction;54
4.3.2;4.2 Model Formulation;55
4.3.3;4.3 Conclusion;56
4.4;5 Le´on-Liern-Vercher’s Model;58
4.4.1;5.1 Formulations of Portfolio Selection Problem;58
4.4.2;5.2 Analysis of Infeasibility of Portfolio Selection Problem;60
4.4.3;5.3 Fuzzy Portfolio Selection Model;61
4.4.4;5.4 Numerical Example;65
4.4.5;5.5 Conclusion;70
4.5;6 Fuzzy Semi-absolute Deviation Portfolio Rebalancing Model;72
4.5.1;6.1 Introduction;72
4.5.2;6.2 Linear Programming Model for Portfolio Rebalancing with Transaction Costs;73
4.5.3;6.3 Portfolio Rebalancing Model based on Fuzzy Decision;76
4.5.4;6.4 Numerical Example;80
4.5.5;6.5 Conclusion;86
4.6;7 Fuzzy Mixed Projects and Securities Portfolio Selection Model;88
4.6.1;7.1 Introduction;88
4.6.2;7.2 Bi-objective Programming Model for Mixed Asset Portfolio Selection;89
4.6.3;7.3 Fuzzy Mixed Asset Portfolio Selection Model;94
4.6.4;7.4 Numerical Example;96
4.6.5;7.5 Conclusion;97
5;Part III Portfolio Selection Models with Interval Coefficients;100
5.1;8 Linear Programming Model with Interval Coefficients;102
5.1.1;8.1 Introduction;102
5.1.2;8.2 Notations and Definitions;103
5.1.3;8.3 The Expected Return Intervals of Securities;104
5.1.4;8.4 The Interval Programming Models for Portfolio Selection;105
5.1.5;8.5 Numerical Example;112
5.1.6;8.6 Conclusion;114
5.2;9 Quadratic Programming Model with Interval Coefficients;116
5.2.1;9.1 Introduction;116
5.2.2;9.2 Crisp Model and Algorithm;116
5.2.3;9.3 The Model with Interval Coefficients and Its Extension;118
5.2.4;9.4 Numerical Example;120
5.2.5;9.5 Conclusion;123
6;Part IV Portfolio Selection Models with Possibility Distribution;124
6.1;10 Tanaka and Guo’s Model with Exponential Possibility Distributions;126
6.1.1;10.1 Introduction;126
6.1.2;10.2 Possibility Distributions in Portfolio Selection Problems;127
6.1.3;10.3 Model Formulation;134
6.1.4;10.4 Numerical Example;135
6.1.5;10.5 Conclusion;137
6.2;11 Carlsson-Fuller-Majlender’s Trapezoidal Possibility Model;140
6.2.1;11.1 Introduction;140
6.2.2;11.2 Model Formulation;141
6.2.3;11.3 Algorithm;147
6.2.4;11.4 Numerical Example;148
6.2.5;11.5 Conclusion;149
6.3;12 Center Spread Model in Fractional Financial Market;152
6.3.1;12.1 Estimation of Possibility Distribution by Using Semi- definite Programming;152
6.3.2;12.2 Model Formulation;153
6.3.3;12.3 Numerical Example;157
6.3.4;12.4 Conclusion;160
7;Part V Fuzzy Passive Portfolio Selection Models;162
7.1;13 Fuzzy Index Tracking Portfolio Selection Model;164
7.1.1;13.1 Introduction;164
7.1.2;13.2 Bi-objective Programming Model for Index Tracking Portfolio Selection;165
7.1.3;13.3 Fuzzy Index Tracking Portfolio Selection Model;167
7.1.4;13.4 Numerical Example;169
7.1.5;13.5 Conclusion;169
8;References;172
9;Subject Index;182