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Foundations of Risk Measurement. I. Risk As Probable Loss

Author

Listed:
  • Peter C. Fishburn

    (Bell Telephone Laboratories, Inc., Murray Hill, New Jersey 07974)

Abstract

This paper seeks to get behind specific contextual referents of risky situations to consider characteristics of risk that apply to many situations. It is guided by previous theoretical and empirical research in perceived risk, and focuses on the joint effects on risk of loss probability and the distribution of losses. The approach taken follows modern axiomatic theory by proposing conditions on a relation "is at least as risky as" between pairs of probability distributions over an outcome variable. Several sets of axioms for risk that characterize different forms for risk measurement are presented.

Suggested Citation

  • Peter C. Fishburn, 1984. "Foundations of Risk Measurement. I. Risk As Probable Loss," Management Science, INFORMS, vol. 30(4), pages 396-406, April.
  • Handle: RePEc:inm:ormnsc:v:30:y:1984:i:4:p:396-406
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    File URL: http://dx.doi.org/10.1287/mnsc.30.4.396
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    Cited by:

    1. Bertrand Maillet & Michele Costola & Massimiliano Caporin & Gregory Jannin, 2015. "On the (Ab)Use of Omega?," Working Papers 2015:02, Department of Economics, University of Venice "Ca' Foscari".
    2. repec:ebl:ecbull:v:4:y:2005:i:16:p:1-9 is not listed on IDEAS
    3. Maurer, Raimond H. & Schlag, Christian, 2002. "Money-back guarantees in individual pension accounts: Evidence from the German pension reform," CFS Working Paper Series 2002/03, Center for Financial Studies (CFS).
    4. Ba Chu, 2012. "Large deviations estimation of the windfall and shortfall probabilities for optimal diversified portfolios," Annals of Finance, Springer, vol. 8(1), pages 97-122, February.
    5. Heckmann, Iris & Comes, Tina & Nickel, Stefan, 2015. "A critical review on supply chain risk – Definition, measure and modeling," Omega, Elsevier, vol. 52(C), pages 119-132.
    6. Ivica Dus & Raimond Maurer & Olivia S. Mitchell, 2005. "Betting on Death and Capital Markets in Retirement: A Shortfall Risk Analysis of Life Annuities," NBER Working Papers 11271, National Bureau of Economic Research, Inc.
    7. Williams, Terry, 1995. "A classified bibliography of recent research relating to project risk management," European Journal of Operational Research, Elsevier, vol. 85(1), pages 18-38, August.
    8. Raimond Mauer & Steffen P. Sebastian, 2002. "Inflation Risk Analysis of European Real Estate Securities," Journal of Real Estate Research, American Real Estate Society, vol. 24(1), pages 47-78.
    9. Robert J. Aumann & Roberto Serrano, 2008. "An Economic Index of Riskiness," Journal of Political Economy, University of Chicago Press, vol. 116(5), pages 810-836, October.
    10. Udo Ebert, 2005. "Measures of downside risk," Economics Bulletin, AccessEcon, vol. 4(16), pages 1-9.
    11. repec:spr:cejnor:v:25:y:2017:i:3:d:10.1007_s10100-016-0458-3 is not listed on IDEAS
    12. Ivica Dus & Raimond Maurer & Olivia S. Mitchell, 2003. "Betting on Death and Capital Markets in Retirement: A Shortfall Risk Analysis of Life Annuities versus Phased Withdrawal Plans," Working Papers wp063, University of Michigan, Michigan Retirement Research Center.
    13. Jianmin Jia & James S. Dyer & John C. Butler, 1999. "Measures of Perceived Risk," Management Science, INFORMS, vol. 45(4), pages 519-532, April.
    14. Robert J. Aumann & Roberto Serrano, 2008. "An Economic Index of Riskiness," Journal of Political Economy, University of Chicago Press, vol. 116(5), pages 810-836, October.
    15. Hentati Rania & Prigent Jean-Luc, 2011. "On the maximization of financial performance measures within mixture models," Statistics & Risk Modeling, De Gruyter, vol. 28(1), pages 63-80, March.
    16. Durbach, Ian N. & Stewart, Theodor J., 2012. "Modeling uncertainty in multi-criteria decision analysis," European Journal of Operational Research, Elsevier, vol. 223(1), pages 1-14.
    17. Bertrand, Philippe & Prigent, Jean-luc, 2011. "Omega performance measure and portfolio insurance," Journal of Banking & Finance, Elsevier, vol. 35(7), pages 1811-1823, July.
    18. Unser, Matthias, 2000. "Lower partial moments as measures of perceived risk: An experimental study," Journal of Economic Psychology, Elsevier, vol. 21(3), pages 253-280, June.
    19. Yang, Jiping & Qiu, Wanhua, 2005. "A measure of risk and a decision-making model based on expected utility and entropy," European Journal of Operational Research, Elsevier, vol. 164(3), pages 792-799, August.
    20. Matos, Manuel A., 2007. "Decision under risk as a multicriteria problem," European Journal of Operational Research, Elsevier, vol. 181(3), pages 1516-1529, September.
    21. Emili Grifell-Tatjé & P. Marquès-Gou, 2002. "Measuring Sustained Superior Performance at the Firm Level," Working Papers 0208, Departament Empresa, Universitat Autònoma de Barcelona, revised Jul 2002.
    22. Durbach, Ian N. & Stewart, Theodor J., 2011. "An experimental study of the effect of uncertainty representation on decision making," European Journal of Operational Research, Elsevier, vol. 214(2), pages 380-392, October.
    23. Chu, Ba & Knight, John & Satchell, Stephen, 2011. "Large deviations theorems for optimal investment problems with large portfolios," European Journal of Operational Research, Elsevier, vol. 211(3), pages 533-555, June.

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    Keywords

    risk measurement; probability of loss;

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