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 studies on risk measurement and capital allocation, which are two important research fields in actuarial science. Empirical studies consider the skew-normal distribution because of its flexibility, interpretability, and tractability. This paper comprises four main sections: an overview of skew-normal distributions; a review of skewness in finance, including asset pricing, portfolio selection, time series modeling, and a review of its applications in insurance, in which the use of alternative distribution functions is widespread. The final section summarizes some of the challenges associated with the use of skew-elliptical distributions and points out some directions for future research. C. Adcock et al.those of Arditti and Levy (1975) and Kraus and Litzenberger (1976), marks the point at which the modern theory of finance started revealing evidence of skewness analogous to that provided by Markowitz, Sharpe, Lintner, Tobin, and others.In the context of actuarial science, it is important to recognize that insurance risks have skewed distributions (see, for example, Lane 2000), which is why in many cases, the classical normal distribution is an inadequate model for insurance risks or losses. Some insurance risks also exhibit heavy tails, especially those exposed to catastrophes (see Embrechts, McNeil, and Straumann 2002). The skew-normal distribution and its extensions thus might be promising since they preserve the advantages of the normal distribution with the additional benefit of flexibility with regard to skewness and kurtosis. The skew-normal distribution and its extensions have been used recently in studies on risk management, capital allocation, and goodness-of-fit (Vernic 2006;Bolance et al. 2008;Eling 2012).This review paper is motivated by the belief that asymmetry in asset returns, and skewness in particular, is an important field of research. Such research has two clear themes. The first is the never-ending and entirely natural wish to develop better univariate models for asset returns. Such model developme...
