Coherent estimation of risk measures

Martin Aichele, Igor Cialenco, Damian Jelito and Marcin Pitera

Papers from arXiv.org

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.

Date: 2025-10
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Persistent link: https://EconPapers.repec.org/RePEc:arx:papers:2510.05809

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