The distortion principle for insurance pricing: properties, identification and robustness

TL;DR

This paper analyzes the properties, robustness, and identification of the distortion principle in insurance pricing, focusing on sensitivity to risk aversion assumptions and ambiguity in loss distributions using Wasserstein distance.

Contribution

It provides new insights into the sensitivity and robustness of distortion functionals and explores methods to identify distortion densities from observed insurance premiums.

Findings

Identifies worst-case distributions under Wasserstein ambiguity.

Analyzes the impact of risk aversion assumptions on distortion premiums.

Proposes methods to infer distortion densities from premium data.

Abstract

Distortion (Denneberg 1990) is a well known premium calculation principle for insurance contracts. In this paper, we study sensitivity properties of distortion functionals w.r.t. the assumptions for risk aversion as well as robustness w.r.t. ambiguity of the loss distribution. Ambiguity is measured by the Wasserstein distance. We study variances of distances for probability models and identify some worst case distributions. In addition to the direct problem we also investigate the inverse problem, that is how to identify the distortion density on the basis of observations of insurance premia.