A decomposition of general premium principles into risk and deviation
Risk Management
2020-12-21 v3 Mathematical Finance
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.
Cite
@article{arxiv.2006.14272,
title = {A decomposition of general premium principles into risk and deviation},
author = {Max Nendel and Frank Riedel and Maren Diane Schmeck},
journal= {arXiv preprint arXiv:2006.14272},
year = {2020}
}