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Über dieses Buch

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.

Inhaltsverzeichnis

Frontmatter

Chapter 1. Preliminaries

Abstract
This chapter presents the preliminaries for the rest of this book. On the one hand, credibility theory and uncertainty theory are outlined, respectively, which provide necessary knowledge for uncertain portfolio optimization. On the other hand, genetic algorithm is reviewed, which is used to solve the portfolio optimization models.
Zhongfeng Qin

Chapter 2. Credibilistic Mean-Variance-Skewness Model

Abstract
Most of the existing works on portfolio optimization have been done based on only the first two moments of return distributions. However, there is a controversy over the issue of whether higher moments should be considered in portfolio selection.
Zhongfeng Qin

Chapter 3. Credibilistic Mean-Absolute Deviation Model

Abstract
Mean-absolute deviation model was first proposed by Konno and Yamazaki (1991) for stochastic portfolio optimization by using absolute deviation risk function to replace variance. It removes most of the difficulties associated with Markowitz’s mean-variance model. This model can cope with large-scale portfolio optimization problem because it leads to a linear programming. Furthermore, the authors showed that this model gave essentially the same results as the mean-variance model if all the returns are normally distributed random variables. Since then, absolute deviation has been accepted as a risk measure. As extensions, Konno et al. (1993) presented mean-absolute deviation-skewness model for the case when the distributions of returns are asymmetrical around their means, and Yu et al. (2010) presented a multiperiod portfolio optimization model with risk control for absolute deviation.
Zhongfeng Qin

Chapter 4. Credibilistic Cross-Entropy Minimization Model

Abstract
Kapur and Kesavan (1992) respectively proposed an entropy maximization model and a cross-entropy minimization model for portfolio optimization. The objective of the first model is to maximize the uncertainty of the random investment return and the second one is to minimize the divergence of the random investment return from a priori one. From then on, many researchers accepted the criterion and investigated these entropy optimization models (Cherny and Maslov 2003; Fang et al. 1997; Rubinstein 2008; Simonelli 2005).
Zhongfeng Qin

Chapter 5. Uncertain Mean-Semiabsolute Deviation Model

Abstract
In the case with lack of historical data, another feasible way is to estimate returns by experts based on their subjective evaluations in the framework of uncertainty theory (Liu 2007). In particular, several researchers have studied portfolio optimization in which security returns are assumed to be uncertain variables. The first attempt is Qin et al. (2009) who formulated the uncertain counterpart of mean-variance model. As extensions, Liu and Qin (2012) proposed an uncertain mean-semiabsolute deviation model for the asymmetric case and Huang and Qiao (2012) presented a risk index model for multi-period case. Different from these, Zhu (2010) applied uncertain optimal control to model continuous-time problem, but Yao and Ji (2014) considered the problem by using uncertain decision making.
Zhongfeng Qin

Chapter 6. Uncertain Mean-LPMs Model

Abstract
Downside risk is a class of risk measures which focuses on the asymmetry of returns about some target level of return (Harlow 1991). It has gradually attracted more and more attentions since investors are often sensitive to downside losses, relative to upside gains. Moreover, it requires simpler theoretical assumptions to justify its application. In portfolio management, investors always prefer securities with smaller downside risk. In the situation with symmetrically distributed returns, some downside risks are consistent with general risk measures. For example, semivariance is exactly proportional to variance for normal distribution, which implies they are equivalent in measuring risk.
Zhongfeng Qin

Chapter 7. Interval Mean-Semiabsolute Deviation Model

Abstract
Most existing researches deal with the expected returns of securities as crisp values, which may be estimated by the experts based on their experience and the historical data. However, since the improper estimations may bring on an unsuccessful investment decision, portfolio experts generally prefer to offer interval estimations instead of crisp point estimations. As early as 1980, Bitran (1980) proposed a linear multiobjective portfolio selection model with interval expected returns. From then on, the interval portfolio selection models were widely studied. For example, Lai et al. (2002) extended the classical mean-semiabsolute deviation model to interval mean-semiabsolute deviation model, Ida (2003) proposed a quadratic interval mean-variance model, Li and Xu (2009) proposed an interval goal programming model on the assumption that security returns are fuzzy variables, and Wu et al. (2013) revisited interval mean-variance analysis by assuming that the expected returns and covariances of assets are both intervals.
Zhongfeng Qin

Chapter 8. Uncertain Random Mean-Variance Model

Abstract
This chapter presents the preliminaries for the rest of this book. On the one hand, credibility theory and uncertainty theory are outlined, respectively, which provide necessary knowledge for uncertain portfolio optimization. On the other hand, genetic algorithm is reviewed, which is used to solve the portfolio optimization models.
Zhongfeng Qin

Chapter 9. Fuzzy Random Mean-Variance Adjusting Model

Abstract
Fuzzy portfolio optimization overemphasizes the experts’ subjective experiences, which results in that it is difficult to accurately estimate security returns. In fact, historical data and subjective experiences may play equally important roles in making investment decisions. This motivates the researchers to investigate the portfolio optimization problem with mixture of randomness and fuzziness such as Huang (2007a) and Gupta et al. (2013). Fuzzy random variable proposed by Kwakernaak (1978) is a useful tool to integrate these two kinds of information. It has actually been applied to many financial optimization problems such as risk model (Huang et al. 2009), risk assessment (Shen and Zhao 2010), life annuity (de Andres-Sanchez and Puchades 2012; Shapiro 2013) and so forth.
Zhongfeng Qin

Chapter 10. Random Fuzzy Mean-Risk Model

Abstract
In practice, the investors may encounter varieties of uncertainties when constructing the optimal portfolio. For example, the probability distributions of security returns may be partially known, which can be described by stochastic returns with not crisp information. We employ fuzzy variables to characterize these information, which implies that security returns are random variables with fuzzy parameters. Liu (2002) proposed the concept of random fuzzy variable to model the case, which is different from fuzzy random variable. From the mathematical viewpoint, a random fuzzy variable is a measurable function from a credibility space to the set of random variables, however a fuzzy random variable is a measurable function from a probability space to the set of fuzzy variables. Although they are different, both of them may describe the portfolio optimization with mixture of randomness and fuzziness.
Zhongfeng Qin

Backmatter

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