Uncertain Portfolio Optimization

ISBN-13: 9789811018091 / Angielski / Twarda / 2016 / 192 str.

Zhongfeng Qin

Opis

This book provides a new modeling approach for portfolio optimization problems involving a lack of sufficient historical data. Considering security returns as different variables, the book presents a series of portfolio optimization models in the framework of credibility theory, uncertainty theory and chance theory, respectively.

Spis treści

Preface

1. Preliminaries

1.1 Credibility Theory

1.1.1 Credibility Measure

1.1.2 Fuzzy Variables

1.1.3 Independence

1.1.4 Expected Value

1.1.5 Variance

1.2 Uncertainty Theory

1.2.1 Uncertain Measure

1.2.2 Uncertain Variable

1.2.3 Uncertainty Distribution

1.2.4 Operational Law

1.2.5 Expected Value

1.3 Genetic Algorithm

2. Credibilistic Mean-Variance-Skewness

2.1 Introduction

2.2 Skewness of Fuzzy Variable

2.3 Mean-Variance-Skewness Model

2.4 Fuzzy Simulation

2.4.1 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

3.4 Fuzzy Simulation for Absolute Deviation

3.5 Numerical Examples

4. 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-Entropy

4.5 Numerical Examples

5. Uncertain Mean-Semiabsolude 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

7.3 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

9.5 Numerical Examples

10. Random Fuzzy Mean-Risk Model

10.1 Introduction

10.2 Random Fuzzy Variable

10.3 Absolute Deviation of Random Fuzzy Variable

10.4 Semivariance of Random Fuzzy Variable

10.5 Random Fuzzy Mean-Risk Models

10.5.1 Random Fuzzy Mean-Absolute Deviation Model

<10.5.2 Random Fuzzy Mean-Semivariance Model

O autorze

Zhongfeng Qin received his BS degree from Nankai University, Tianjin, China and his PhD degree in Operations Research and Cybernetics from Tsinghua University, Beijing, China. He is currently an associate professor at the School of Economics and Management at Beihang University, Beijing, China. His current research interests include uncertain modeling and optimization, portfolio optimization and risk modeling. He was awarded “New Century Excellent Talents in University of the Ministry of Education” in 2012. Also, he was honored with the “7th Jiaqing Zhong Prize on Operations Research” and the “9th Outstanding New Scholar on Operations Research” award.

Blurb

This book provides a new modeling approach for portfolio optimization problems involving a lack of sufficient historical data. The content mainly reflects the author’s extensive work on uncertainty portfolio optimization in recent years. Considering security returns as different variables, the book presents a series of portfolio optimization models in the framework of credibility theory, uncertainty theory and chance theory, respectively. As such, it offers readers a comprehensive and up-to-date guide to uncertain portfolio optimization models.