Premium Calculation by Transforming the Layer Premium Density

This paper examines a class of premium functionals which are 0) ecomonotomic additive and (u) stochastic dominance preservative. The representation for this class is a transformation of the decumulative distribution function. It holds close connections with the recent developments in economic decision theory and non-additive measure theory. Among a few elementary members of this class, the pronominal hazard transform seems to stand out as being most plausible for actuaries.