Coherent estimation of risk measures
Coherent estimation of risk measures ArXiv ID: 2510.05809 “View on arXiv” Authors: Martin Aichele, Igor Cialenco, Damian Jelito, Marcin Pitera Abstract We develop a statistical framework for risk estimation, inspired by the axiomatic theory of risk measures. Coherent risk estimators – functionals of P&L samples inheriting the economic properties of risk measures – are defined and characterized through robust representations linked to $L$-estimators. The framework provides a canonical methodology for constructing estimators with sound financial and statistical properties, unifying risk measure theory, principles for capital adequacy, and practical statistical challenges in market risk. A numerical study illustrates the approach, focusing on expected shortfall estimation under both i.i.d. and overlapping samples relevant for regulatory FRTB model applications. ...