Convex Risk Measures for the Aggregation of Multiple Information Sources and Applications in Insurance

TL;DR

This paper introduces a new class of convex risk measures based on the Fréchet mean to effectively aggregate multiple information sources, providing robust risk assessment tools for insurance applications.

Contribution

It develops a novel convex risk measure framework that aggregates multiple information sources using the Fréchet mean, with closed-form expressions for practical risk management.

Findings

Risk measures can be expressed in closed analytic forms.

The measures enable qualitative interpretations and comparative statics.

Applications include capital risk allocation and premium calculation.

Abstract

We propose a novel class of convex risk measures, based on the concept of the Fr\'echet mean, designed in order to handle uncertainty which arises from multiple information sources regarding the risk factors of interest. The proposed risk measures robustly characterize the exposure of the firm, by filtering out appropriately the partial information available in individual sources into an aggregate model for the risk factors of interest. Importantly, the proposed risks can be expressed in closed analytic forms allowing for interesting qualitative interpretations as well as comparative statics and thus facilitate their use in the everyday risk management process of the insurance firms. The potential use of the proposed risk measures in insurance is illustrated by two concrete applications, capital risk allocation and premia calculation under uncertainty.