Before revision: In this paper, we provide an axiomatic approach to general premium principles giving rise to a decomposition into risk , as a generalization of the expected value, and deviation , as a generalization of the variance.
After revision: In this paper, we provide an axiomatic approach to general premium principles in a probability-free setting that allows for Knightian uncertainty. Every premium principle is the sum of a risk measure , as a generalization of the expected value, and deviation , as a generalization of the variance.