First Step: In Terms of Distortion Functions Sample Clauses

First Step: In Terms of Distortion Functions. ‌ The first crucial step of solving Problem (2.3.8) is to express the risk measures in terms of some distortion functions. In particular, define  gα(λ) =o  λ 1−α ∧ 1, ∀λ ∈ [0, 1] if α ∈ [0, 1), 1, ∀λ ∈ [0, 1] if α = 1. This step is composed of several representation results, which will be recalled in the following lemmas. Before presenting the first lemma, we prove another lemma which depicts that the TVaR of a non-negative random variable can be rewritten as a distortion risk measure with the above distortion function gα, which is a standard result in the literature.
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