Fuzzy Portfolio Optimization: Theory and Methods

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Springer Science & Business Media, Sep 20, 2008 - Business & Economics - 176 pages
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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.
 

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Contents

Survey for Portfolio Selection Under Fuzzy Uncertain Circumstances
3
12 Portfolio Selection Based on the Fuzzy Decision Theory
5
13 Portfolio Selection Based on Possibilistic Programming
7
131 The CenterSpread Model
8
132 Models Using the Necessity Measure
10
14 Portfolio Selection Based on Interval Programming
13
Portfolio Selection Models Based on Fuzzy Decision Making
16
Fuzzy Decision Making and Maximization Decision Making
19
Linear Programming Model with Interval Coefficients
93
82 Notations and Definitions
94
83 The Expected Return Intervals of Securities
95
84 The Interval Programming Models for Portfolio Selection
96
85 Numerical Example
103
86 Conclusion
105
Quadratic Programming Model with Interval Coefficients
107
93 The Model with Interval Coefficients and Its Extension
109

Portfolio Selection Model with Fuzzy Liquidity Constraints
21
32 Minimax Semiabsolute Deviation Risk Function
22
33 Fuzzy Liquidity of Securities
23
34 Model Formulation
25
35 Numerical Example
37
36 Conclusion
39
Ramaswamys Model
44
42 Model Formulation
46
43 Conclusion
47
LeónLiernVerchers Model
49
52 Analysis of Infeasibility of Portfolio Selection Problem
51
53 Fuzzy Portfolio Selection Model
52
54 Numerical Example
56
55 Conclusion
61
Fuzzy Semiabsolute Deviation Portfolio Rebalancing Model
62
62 Linear Programming Model for Portfolio Rebalancing with Transaction Costs
64
63 Portfolio Rebalancing Model based on Fuzzy Decision
67
64 Numerical Example
71
65 Conclusion
77
Fuzzy Mixed Projects and Securities Portfolio Selection Model
79
72 Biobjective Programming Model for Mixed Asset Portfolio Selection
80
73 Fuzzy Mixed Asset Portfolio Selection Model
85
74 Numerical Example
87
75 Conclusion
88
Portfolio Selection Models with Interval Coefficients
90
94 Numerical Example
111
95 Conclusion
114
Portfolio Selection Models with Possibility Distribution
115
Tanaka and Guos Model with Exponential Possibility Distributions
116
102 Possibility Distributions in Portfolio Selection Problems
118
103 Model Formulation
125
104 Numerical Example
126
105 Conclusion
128
CarlssonFullérMajlenders Trapezoidal Possibility Model
131
112 Model Formulation
132
113 Algorithm
138
114 Numerical Example
139
115 Conclusion
140
Center Spread Model in Fractional Financial Market
142
122 Model Formulation
144
123 Numerical Example
148
124 Conclusion
151
Fuzzy Passive Portfolio Selection Models
153
Fuzzy Index Tracking Portfolio Selection Model
155
132 Biobjective Programming Model for Index Tracking Portfolio Selection
156
133 Fuzzy Index Tracking Portfolio Selection Model
158
134 Numerical Example
160
References
162
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