Coherent Risk Measures Derived from Utility Functions

  • Yuji YoshidaEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11144)


Coherent risk measures in financial management are discussed from the view point of average value-at-risks with risk spectra. A minimization problem of the distance between risk estimations through decision maker’s utility and coherent risk measures with risk spectra is introduced. The risk spectrum of the optimal coherent risk measures in this problem is obtained and it inherits the risk averse property of utility functions. Various properties of coherent risk measures and risk spectrum are demonstrated. Several numerical examples are given to illustrate the results.



This research is supported from JSPS KAKENHI Grant Number JP 16K05282.


  1. 1.
    Acerbi, C.: Spectral measures of risk: a coherent representation of subjective risk aversion. J. Bank. Financ. 26, 1505–1518 (2002)CrossRefGoogle Scholar
  2. 2.
    Adam, A., Houkari, M., Laurent, J.-P.: Spectral risk measures and portfolio selection. J. Bank. Financ. 32, 1870–1882 (2008)CrossRefGoogle Scholar
  3. 3.
    Artzner, P., Delbaen, F., Eber, J.-M., Heath, D.: Coherent measures of risk. Math. Financ. 9, 203–228 (1999)MathSciNetCrossRefGoogle Scholar
  4. 4.
    Cotter, J., Dowd, K.: Extreme spectral risk measures: an application to futures clearinghouse margin requirements. J. Bank. Financ. 30, 3469–3485 (2006)CrossRefGoogle Scholar
  5. 5.
    Emmer, S., Kratz, M., Tasche, D.: What is the best risk measure in practice? A comparison of standard measures. J. Risk 18, 31–60 (2015)CrossRefGoogle Scholar
  6. 6.
    Javidi, A.A.: Entropic value-at-risk: a new coherent risk measure. J. Optim. Theory Appl. 155, 1105–1123 (2012)MathSciNetCrossRefGoogle Scholar
  7. 7.
    Jorion, P.: Value at Risk: The New Benchmark for Managing Financial Risk. McGraw-Hill, New York (2006)Google Scholar
  8. 8.
    Kusuoka, S.: On law-invariant coherent risk measures. Adv. Math. Econ. 3, 83–95 (2001)MathSciNetCrossRefGoogle Scholar
  9. 9.
    Markowitz, H.: Mean-Variance Analysis in Portfolio Choice and Capital Markets. Blackwell, Oxford (1990)zbMATHGoogle Scholar
  10. 10.
    Pratt, J.W.: Risk aversion in the small and the large. Econometrica 32, 122–136 (1964)CrossRefGoogle Scholar
  11. 11.
    Rockafellar, R.T., Uryasev, S.: Optimization of conditional value-at-risk. J. Risk 2, 21–41 (2000)CrossRefGoogle Scholar
  12. 12.
    Tasche, D.: Expected shortfall and beyond. J. Bank. Financ. 26, 1519–1533 (2002)CrossRefGoogle Scholar
  13. 13.
    Yaari, M.E.: The dual theory of choice under risk. Econometrica 55, 95–115 (1987)MathSciNetCrossRefGoogle Scholar
  14. 14.
    Yoshida, Y.: A dynamic value-at-risk portfolio model. In: Torra, V., Narakawa, Y., Yin, J., Long, J. (eds.) MDAI 2011. LNCS (LNAI), vol. 6820, pp. 43–54. Springer, Heidelberg (2011). Scholar
  15. 15.
    Yoshida, Y.: An Ordered Weighted Average with a Truncation Weight on Intervals. In: Torra, V., Narukawa, Y., López, B., Villaret, M. (eds.) MDAI 2012. LNCS (LNAI), vol. 7647, pp. 45–55. Springer, Heidelberg (2012). Scholar

Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  1. 1.Faculty of Economics and Business AdministrationUniversity of KitakyushuKitakyushuJapan

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