A decomposition of general premium principles into risk and deviation

TL;DR

This paper introduces a new axiomatic framework for premium principles that decomposes them into risk and deviation components, accommodating Knightian uncertainty and linking to market consistency.

Contribution

It provides a novel decomposition of premium principles into risk and deviation measures within a probability-free setting, extending previous axiomatizations.

Findings

Unique maximal risk and minimal deviation measures identified.

Embedding of previous axiomatizations into the new framework.

Analysis of dual representations and market consistency.

Abstract

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.