What Is a Good Risk Measure: Bridging the Gaps Between Data, Coherent Risk Measures, and Insurance Risk Measures

Choosing a proper risk measure is of great regulatory importance, as exemplified in Basel Accord that uses Value-at-Risk (VaR) in combination with scenario analysis as a preferred risk measure. The main motivation of this paper is to investigate whether VaR, in combination with scenario analysis, is a good risk measure for external regulation. While many risk measures may be suitable for internal management, we argue that risk measures used for external regulation should have robustness with respect to modeling assumptions and data. We propose new data-based risk measures called natural risk statistics that are characterized by a new set of axioms based on the comonotonicity from decision theory. Natural risk statistics include VaR as a special case and therefore provide a theoretical basis for using VaR along with scenario analysis as a robust risk measure for the purpose of external, regulatory risk measurement.