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Tail Value-at-Risk-Based Expectiles for Extreme Risks and Their Application in Distributionally Robust Portfolio Selections

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  • Haoyu Chen

    (School of Data Science, University of Science and Technology of China, Hefei 230000, China)

  • Kun Fan

    (Key Laboratory of Advanced Theory and Application in Statistics and Data Science-MOE, School of Statistics, East China Normal University, 3663 North Zhongshan Road, Shanghai 200062, China)

Abstract

Empirical evidence suggests that financial risk has a heavy-tailed profile. Motivated by recent advances in the generalized quantile risk measure, we propose the tail value-at-risk (TVaR)-based expectile, which can capture the tail risk compared with the classic expectile. In addition to showing that the risk measure is well-defined, the properties of TVaR-based expectiles as risk measures were also studied. In particular, we give the equivalent characterization of the coherency. For extreme risks, usually modeled by a regularly varying survival function, the asymptotic expansion of a TVaR-based expectile (with respect to quantiles) was studied. In addition, motivated by recent advances in distributionally robust optimization in portfolio selections, we give the closed-form of the worst-case TVaR-based expectile based on moment information. Based on this closed form of the worst-case TVaR-based expectile, the distributionally robust portfolio selection problem is reduced to a convex quadratic program. Numerical results are also presented to illustrate the performance of the new risk measure compared with classic risk measures, such as tail value-at-risk-based expectiles.

Suggested Citation

  • Haoyu Chen & Kun Fan, 2022. "Tail Value-at-Risk-Based Expectiles for Extreme Risks and Their Application in Distributionally Robust Portfolio Selections," Mathematics, MDPI, vol. 11(1), pages 1-16, December.
    • Handle: RePEc:gam:jmathe:v:11:y:2022:i:1:p:91-:d:1015106
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    References listed on IDEAS

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