Mean-variance-skewness model for portfolio selection with fuzzy returns

Mean-semivariance models for fuzzy portfolio selection

Neural network-based mean-variance-skewness model for portfolio selection

Portfolio selection based on fuzzy cross-entropy

That the returns on financial assets and insurance claims are not well described by the multivariate normal distribution is generally acknowledged in the literature. This paper presents a review of the use of the skew-normal distribution and its extensions in finance and actuarial science, highlighting known results as well as potential directions for future research. When skewness and kurtosis are present in asset returns, the skew-normal and skew-Student distributions are natural candidates in both theoretical and empirical work. Their parameterization is parsimonious and they are mathematically tractable. In finance, the distributions are interpretable in terms of the efficient markets hypothesis. Furthermore, they lead to theoretical results that are useful for portfolio selection and asset pricing. In actuarial science, the presence of skewness and kurtosis in insurance claims data is the main motivation for using the skew-normal distribution and its extensions. The skew-normal has been used in studi...

Skewed distributions in finance and actuarial science: a review

The mean-variance methodology originally proposed by Markowitz (1952) plays a crucial role in the theory of portfolio selection and gains widespread acceptance as a practical tool for portfolio optimization. Since the seminal works of Markowitz, numerous studies on portfolio selection and performance measures have been made based on only the first two moments of return distributions. However, there is a controversy over the issue of whether higher moments should be accounted for in portfolio selection. Many authors (e.g., [Arditti (1967,1971), Samuelson (1958), Rubinstein (1973), Konno et al. (1995)]) argued that the higher moments can not be neglected unless there is a reason to believe that the asset returns are normally distributed and the utility function is quadratic, or that the higher moments are irrelevant to the investor’s decision.

S. Liu

Papers

Mean-variance-skewness model for portfolio selection with transaction costs