On a robust risk measurement approach for capital determination errors minimization

TL;DR

This paper introduces a robust risk measurement method that minimizes combined overestimation and underestimation costs under uncertainty, with theoretical guarantees and an empirical application in capital determination.

Contribution

It presents a novel robust risk measurement framework considering multiple probability measures, linking to coherent risk measures, and demonstrating practical application in capital setting.

Findings

Existence of solutions is guaranteed.

The approach relates to coherent risk measures.

Empirical results illustrate practical effectiveness.

Abstract

We propose a robust risk measurement approach that minimizes the expectation of overestimation plus underestimation costs. We consider uncertainty by taking the supremum over a collection of probability measures, relating our approach to dual sets in the representation of coherent risk measures. We provide results that guarantee the existence of a solution and explore the properties of minimizer and minimum as risk and deviation measures, respectively. An empirical illustration is carried out to demonstrate the use of our approach in capital determination.