Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Dual Representation of Expectile based Expected Shortfall and Its
  Properties   The expectile can be considered as a generalization of 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
quantile. We provide its dual representation in terms of Bochner integral.
Among other properties, we show that it is bounded from below in terms of
convex combinations of expected shortfalls, and also from above by the smallest
law invariant, coherent and comonotonic risk measure, 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 compute explicitly the expectile based expected shortfall
for some selected class of distributions.

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The categories of this paper are: mtrl-th
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The categories of this paper are: q-alg
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The categories of this paper are: gr-qc
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The categories of this paper are: q-bio
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The categories of this paper are: hep-ex
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The categories of this paper are: physics
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The categories of this paper are: quant-ph
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The categories of this paper are: cond-mat
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The categories of this paper are: chem-ph
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The categories of this paper are: math
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The categories of this paper are: funct-an
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The categories of this paper are: cmp-lg
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The categories of this paper are: adap-org
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The categories of this paper are: stat
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The categories of this paper are: bayes-an
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The categories of this paper are: eess