{"ID":2859290,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2510.05809","arxiv_id":"2510.05809","title":"Coherent estimation of risk measures","abstract":"We develop a statistical framework for risk estimation, inspired by the axiomatic theory of risk measures. Coherent risk estimators -- functionals of P\\\u0026L 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. Numerical illustrations based on simulated and market data demonstrate that coherence of a risk measure does not necessarily carry over to its estimators and show that alternative admissible weight structures within the CRE representation can lead to substantially different capital adequacy outcomes.","short_abstract":"We develop a statistical framework for risk estimation, inspired by the axiomatic theory of risk measures. Coherent risk estimators -- functionals of P\\\u0026L samples inheriting the economic properties of risk measures -- are defined and characterized through robust representations linked to $L$-estimators. The framework p...","url_abs":"https://arxiv.org/abs/2510.05809","url_pdf":"https://arxiv.org/pdf/2510.05809v4","authors":"[\"Martin Aichele\",\"Igor Cialenco\",\"Damian Jelito\",\"Marcin Pitera\"]","published":"2025-10-07T11:25:35Z","proceeding":"q-fin.RM","tasks":"[\"q-fin.RM\",\"math.ST\",\"q-fin.ST\"]","methods":"[]","has_code":false}