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The Axiomatic Approach to Risk Measures for Capital Determination

Author

Listed:
  • Hans Föllmer

    (Institut für Mathematik, Humboldt-Universität zu Berlin, 10099 Berlin, Germany)

  • Stefan Weber

    (Institut für Mathematische Stochastik, Leibniz Universität Hannover, 30167 Hannover, Germany)

Abstract

The quantification of downside risk in terms of capital requirements is a key issue for both regulators and the financial industry. This review presents the axiomatic approach, which is based on monetary risk measures. These provide a unifying mathematical framework for the determination of capital requirements, for economic indices of riskiness, and for the analysis of preferences in the face of risk and Knightian uncertainty. In the special case of distribution-based risk measures, we review recent advances in characterizing their statistical properties such as elicitability and robustness.

Suggested Citation

  • Hans Föllmer & Stefan Weber, 2015. "The Axiomatic Approach to Risk Measures for Capital Determination," Annual Review of Financial Economics, Annual Reviews, vol. 7(1), pages 301-337, December.
    • Handle: RePEc:anr:refeco:v:7:y:2015:p:301-337
    DOI: 10.1146/annurev-financial-111914-042031
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    More about this item

    Keywords

    capital requirements; elicitability; indices of riskiness; monetary risk measures; robustness; variational preferences;
    All these keywords.

    JEL classification:

    • C44 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Operations Research; Statistical Decision Theory
    • C5 - Mathematical and Quantitative Methods - - Econometric Modeling
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
    • G01 - Financial Economics - - General - - - Financial Crises
    • G1 - Financial Economics - - General Financial Markets
    • G2 - Financial Economics - - Financial Institutions and Services

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