2025/10/07 by Aichele, Martin, Cialenco, Igor, Jelito, Damian +1
#62G05 #91B05 #91G70 #FOS: Economics and business #FOS: Mathematics #Risk Management (q-fin.RM) #Statistical Finance (q-fin.ST) #Statistics Theory (math.ST)
paper · doi:10.48550/arxiv.2510.05809
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.