An expectile can be considered a generalization of a quantile.While expected shortfall is a quantile-based risk measure,we study its counterpart-the expectile-based expected shortfall-where expectile takes the place o...An expectile can be considered a generalization of a quantile.While expected shortfall is a quantile-based risk measure,we study its counterpart-the expectile-based expected shortfall-where expectile takes the place of a quantile.We provide its dual representation in terms of a Bochner integral.Among other properties,we show that it is bounded from below in terms of the convex combination of expected shortfalls,and also from above by the smallest law invariant,coherent,and comonotonic risk measures,for which we give the explicit formulation of the corresponding distortion function.As a benchmark to the industry standard expected shortfall,we further provide its comparative asymptotic behavior in terms of extreme value distributions.Based on these results,we finally explicitly compute the expectile-based expected shortfall for selected classes of distributions.展开更多
基金This research is supported by National Science Foundation of China(Grant No.11971310,11671257)“Assessment of Risk and Uncertainty in Finance”(Grant No.AF0710020)from Shanghai Jiao Tong University.
文摘An expectile can be considered a generalization of a quantile.While expected shortfall is a quantile-based risk measure,we study its counterpart-the expectile-based expected shortfall-where expectile takes the place of a quantile.We provide its dual representation in terms of a Bochner integral.Among other properties,we show that it is bounded from below in terms of the convex combination of expected shortfalls,and also from above by the smallest law invariant,coherent,and comonotonic risk measures,for which we give the explicit formulation of the corresponding distortion function.As a benchmark to the industry standard expected shortfall,we further provide its comparative asymptotic behavior in terms of extreme value distributions.Based on these results,we finally explicitly compute the expectile-based expected shortfall for selected classes of distributions.
