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Coherent estimation of risk measures

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  • 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.

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  • Martin Aichele & Igor Cialenco & Damian Jelito & Marcin Pitera, 2025. "Coherent estimation of risk measures," Papers 2510.05809, arXiv.org, revised Dec 2025.
    • Handle: RePEc:arx:papers:2510.05809
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    References listed on IDEAS

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    1. Acerbi, Carlo, 2002. "Spectral measures of risk: A coherent representation of subjective risk aversion," Journal of Banking & Finance, Elsevier, vol. 26(7), pages 1505-1518, July.
    2. Acerbi, Carlo & Tasche, Dirk, 2002. "On the coherence of expected shortfall," Journal of Banking & Finance, Elsevier, vol. 26(7), pages 1487-1503, July.
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