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 a deviation measure, as a generalization of the variance. One can uniquely identify a maximal risk measure and a minimal deviation measure in such decompositions. We show how previous axiomatizations of premium principles can be embedded into our more general framework. We discuss dual representations of convex premium principles, and study the consistency of premium principles with a financial market in which insurance contracts are traded.

我们在允许奈特不确定性的无概率设置中提供了一般保费原则的公理化方法。每个溢价原则都是风险度量（作为预期值的概括）和偏差度量（作为方差的概括）的总和。在这种分解中，可以唯一地识别最大风险度量和最小偏差度量。我们展示了如何将溢价原则的先前公理化嵌入到我们更通用的框架中。我们讨论凸保费原则的双重表示，并研究保费原则与保险合同交易的金融市场的一致性。