Tail Conditional Expectation and Tail Variance for Extended Generalized Skew-Elliptical Distributions

Pin Wang, Guojing Wang, Yang Yang and Jing Yao ()
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Pin Wang: Center for Financial Engineering and Department of Mathematics, Soochow University, Suzhou 215006, China
Guojing Wang: Center for Financial Engineering and Department of Mathematics, Soochow University, Suzhou 215006, China
Yang Yang: Center for Financial Engineering and Department of Mathematics, Soochow University, Suzhou 215006, China
Jing Yao: Center for Financial Engineering and Department of Mathematics, Soochow University, Suzhou 215006, China

Mathematics, 2025, vol. 13, issue 18, 1-24

Abstract: This study derives explicit expressions for the Tail Conditional Expectation (TCE) and Tail Variance (TV) within the framework of the extended generalized skew-elliptical (EGSE) distribution. The EGSE family generalizes the class of elliptical distributions by incorporating a selection method, thereby allowing simultaneous and flexible control over location, scale, skewness, and tail heaviness in a unified parametric setting. As notable special cases, our results encompass the extended skew-normal, extended skew-Student- t , extended skew-logistic, and extended skew-Laplace distributions. The derived formulas extend existing results for generalized skew-elliptical distributions and reduce, to a considerable extent, the reliance on numerical integration, thus enhancing their tractability for actuarial and financial risk assessment. The practical utility of the proposed framework is further illustrated through an empirical analysis based on real stock market data, highlighting its effectiveness in quantifying and contrasting the heterogeneous tail risk profiles of financial assets.

Keywords: extended generalized skew-elliptical distributions; risk measure; Tail Conditional Expectation; tail variance (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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