Abstract
In this chapter, the authors introduce a modern approach to pricing, where the risk and margin are compared to supporting capital rather than expected loss. A capital-centric view leads naturally to pricing by layer, a layer pricing distortion function, and finally, an associated spectral risk measure. The authors derive the distortion function's properties from its interpretation as a set of layer prices. They explain how to interpret a distortion function as a risk-adjusted probability and show how to use it to compute standard insurance statistics. The authors summarize basic insurance market statistics for Bernoulli layers and then analyze the pricing of non-Bernoulli risks by showing how to integrate the premium layer density. They define the spectral risk measure (SRM) associated with a concave distortion function and relate the properties of the distortion and SRM.
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