Uncertain portfolio optimization /
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| Format: | eBook |
| Language: | English |
| Published: |
Singapore :
Springer,
[2016]
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| Series: | Uncertainty and operations research.
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| Subjects: | |
| Online Access: | Connect to the full text of this electronic book |
Table of Contents:
- Preface; Acknowledgment; Contents; 1 Preliminaries; 1.1 Credibility Theory; 1.1.1 Credibility Measure; 1.1.2 Fuzzy Variable; 1.1.3 Membership Function; 1.1.3.1 Simple Fuzzy Variable; 1.1.3.2 Equipossible Fuzzy Variable; 1.1.3.3 Triangular Fuzzy Variable; 1.1.3.4 Trapezoidal Fuzzy Variable; 1.1.3.5 Normal Fuzzy Variable; 1.1.3.6 Exponential Fuzzy Variable; 1.1.4 Credibility Distribution; 1.1.5 Independence; 1.1.6 Expected Value; 1.1.7 Variance; 1.2 Uncertainty Theory; 1.2.1 Uncertain Measure; 1.2.2 Uncertain Variable; 1.2.2.1 Independence; 1.2.3 Uncertainty Distribution
- 1.2.3.1 Linear Uncertainty Distribution1.2.3.2 Zigzag Uncertainty Distribution; 1.2.3.3 Normal Uncertainty Distribution; 1.2.3.4 Regular Uncertainty Distribution; 1.2.3.5 Inverse Uncertainty Distribution; 1.2.4 Operational Law; 1.2.5 Expected Value; 1.3 Genetic Algorithm; 1.3.1 Representation Structure; 1.3.2 Initialization Process; 1.3.3 Evaluation Function; 1.3.4 Selection Process; 1.3.5 Crossover Operation; 1.3.6 Mutation Operation; 1.3.7 Genetic Algorithm; 2 Credibilistic Mean-Variance-Skewness Model; 2.1 Introduction; 2.2 Skewness of Fuzzy Variable; 2.3 Mean-Variance-Skewness Model
- 2.4 Fuzzy Simulation2.4.1 Fuzzy Simulation for Credibility; 2.4.2 Fuzzy Simulation for Expected Value; 2.4.3 Fuzzy Simulation for Skewness; 2.5 Numerical Examples; 3 Credibilistic Mean-Absolute Deviation Model; 3.1 Introduction; 3.2 Absolute Deviation of Fuzzy Variable; 3.3 Mean-Absolute Deviation Model; 3.3.1 Credibility Mean-Absolute Deviation-Skewness Model; 3.4 Fuzzy Simulation for Absolute Deviation; 3.5 Numerical Examples; 4 Credibilistic Cross-Entropy Minimization Model; 4.1 Introduction; 4.2 Cross-Entropy of Fuzzy Variable; 4.3 Credibilistic Cross-Entropy Minimization Model
- 4.4 Fuzzy Simulation for Cross-Entropy4.5 Numerical Examples; 5 Uncertain Mean-Semiabsolute Deviation Model; 5.1 Introduction; 5.2 Semiabsolute Deviation of Uncertain Variable; 5.3 Mean-Semiabsolute Deviation Model; 5.4 Mean-Semiabsolute Deviation Adjusting Model; 5.5 Numerical Examples; 6 Uncertain Mean-LPMs Model; 6.1 Introduction; 6.2 Lower Partial Moments of Uncertain Variable; 6.3 Uncertain Mean-LPMs Model; 6.4 Numerical Examples; 7 Interval Mean-Semiabsolute Deviation Model; 7.1 Introduction; 7.2 Uncertainty Generation Theorem; 7.2.1 Maximum Uncertainty Principle
- 7.3 Mean-Semiabsolute Deviation Model7.3.1 Distribution Function; 7.3.2 Expected Value; 7.3.3 Semiabsolute Deviation; 7.3.4 Uncertain Mean-Semiabsolute Deviation Model; 7.4 Numerical Examples; 8 Uncertain Random Mean-Variance Model; 8.1 Introduction; 8.2 Uncertain Random Variable; 8.3 Problem Statement; 8.4 Model Formulation; 8.5 Numerical Examples; 9 Fuzzy Random Mean-Variance Adjusting Model; 9.1 Introduction; 9.2 Fuzzy Random Variable; 9.3 Mean-Variance Adjusting Model; 9.4 Equivalent Crisp Models; 9.4.1 Case I: Simple Fuzzy Random Return; 9.4.2 Case II: Triangular Fuzzy Random Return