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Expectiles and quantiles can both be defined as the solution of minimization problems. Contrary to quantiles though, expectiles are determined by tail expectations rather than tail probabilities, and define a coherent risk measure. For these two reasons in particular, expectiles have recently started to be considered as serious candidates to become standard tools in actuarial and financial risk management...
We use tail expectiles to estimate alternative measures to the value at risk and marginal expected shortfall, which are two instruments of risk protection of utmost importance in actuarial science and statistical finance. The concept of expectiles is a least squares analogue of quantiles. Both are M‐quantiles as the minimizers of an asymmetric convex loss function, but expectiles are the only M‐quantiles...
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