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In this paper we calculate premiums which are based on the minimization of the Expected Tail Loss or Conditional Tail Expectation (CTE) of absolute loss functions. The methodology generalizes well known premium calculation procedures and gives sensible results in practical applications. The choice of the absolute loss becomes advisable in this context since its CTE is easy to calculate and to understand in intuitive terms. The methodology also can be applied to the calculation of the VaR and CTE of the loss associated with a given premium.