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An Extended Family of Financial-Risk Measures


  • Christian S. Pedersen

    (Trinity College, Cambridge University, Cambridge, U.K CB2 ITQ)

  • Stephen E. Satchell

    (Trinity College, Cambridge University, Cambridge, U.K CB2 ITQ)


Recalling the class of risk measures introduced by Stone [1973], the authors survey measures from different academic disciplines—including psychology, operations research, management science, economics, and finance—that have been introduced since 1973. We introduce a general class of risk measures that extends Stone's class to include these new measures. Finally, we give four axioms that describe necessary attributes of a good financial risk measure and show which of the measures surveyed satisfy these. We demonstrate that all measures that satisfy our axioms, as well as those that do not but are commonly used in finance, belong to our new generalized class. The Geneva Papers on Risk and Insurance Theory (1998) 23, 89–117. doi:10.1023/A:1008665926432

Suggested Citation

  • Christian S. Pedersen & Stephen E. Satchell, 1998. "An Extended Family of Financial-Risk Measures," The Geneva Risk and Insurance Review, Palgrave Macmillan;International Association for the Study of Insurance Economics (The Geneva Association), vol. 23(2), pages 89-117, December.
  • Handle: RePEc:pal:genrir:v:23:y:1998:i:2:p:89-117

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    Cited by:

    1. Cillo, Alessandra & Delquié, Philippe, 2014. "Mean-risk analysis with enhanced behavioral content," European Journal of Operational Research, Elsevier, vol. 239(3), pages 764-775.
    2. Bertrand, Philippe & Prigent, Jean-luc, 2011. "Omega performance measure and portfolio insurance," Journal of Banking & Finance, Elsevier, vol. 35(7), pages 1811-1823, July.
    3. Schuhmacher, Frank & Auer, Benjamin R., 2014. "Sufficient conditions under which SSD- and MR-efficient sets are identical," European Journal of Operational Research, Elsevier, vol. 239(3), pages 756-763.
    4. Schuhmacher, Frank & Eling, Martin, 2012. "A decision-theoretic foundation for reward-to-risk performance measures," Journal of Banking & Finance, Elsevier, vol. 36(7), pages 2077-2082.
    5. Jordi Andreu & Salvador Torra, 2009. "Optimal market indices using value-at-risk: a first empirical approach for three stock markets," Applied Financial Economics, Taylor & Francis Journals, vol. 19(14), pages 1163-1170.
    6. repec:ebl:ecbull:v:4:y:2005:i:16:p:1-9 is not listed on IDEAS
    7. Albrecht, Peter, 2003. "Risk measures," Papers 03-01, Sonderforschungsbreich 504.
    8. Ben Ameur, H. & Prigent, J.L., 2014. "Portfolio insurance: Gap risk under conditional multiples," European Journal of Operational Research, Elsevier, vol. 236(1), pages 238-253.
    9. Hurlimann, Werner, 2006. "A note on generalized distortion risk measures," Finance Research Letters, Elsevier, vol. 3(4), pages 267-272, December.
    10. Thierry Chauveau & Sylvain Friederich & Jérôme Héricourt & Emmanuel Jurczenko & Catherine Lubochinsky & Bertrand Maillet & Christophe Moussu & Bogdan Négréa & Hélène Raymond-Feingold, 2004. "La volatilité des marchés augmente-t-elle ?," Revue d'Économie Financière, Programme National Persée, vol. 74(1), pages 17-44.
    11. Kaluszka, Marek, 2004. "An extension of Arrow's result on optimality of a stop loss contract," Insurance: Mathematics and Economics, Elsevier, vol. 35(3), pages 527-536, December.
    12. Carsten Lausberg & Stephen Lee & Moritz Müller & Cay Oertel & Tobias Schultheiß, 2020. "Risk measures for direct real estate investments with non-normal or unknown return distributions," Zeitschrift für Immobilienökonomie (German Journal of Real Estate Research), Springer;Gesellschaft für Immobilienwirtschaftliche Forschung e. V., vol. 6(1), pages 3-27, April.

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