Dynamic Average Value-at-Risk Allocation on Worst Scenarios in Asset Management

  • Yuji YoshidaEmail author
  • Satoru Kumamoto
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11436)


A dynamic portfolio optimization model with average value-at-risks is discussed for drastic declines of asset prices. Analytical solutions for the optimization at each time are obtained by mathematical programming. By dynamic programming, an optimality equation for optimal average value-at-risks over time is derived. The optimal portfolios and the corresponding average value-at-risks are given as solutions of the optimality equation. A numerical example is given to understand the solutions and the results.



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


  1. 1.
    Artzner, P., Delbaen, F., Eber, J.-M., Heath, D.: Coherent measures of risk. Math. Finance 9, 203–228 (1999)MathSciNetCrossRefGoogle Scholar
  2. 2.
    El Chaoui, L., Oks, M., Oustry, F.: Worst-case value at risk and robust portfolio optimization: a conic programming approach. Oper. Res. 51, 543–556 (2003)MathSciNetCrossRefGoogle Scholar
  3. 3.
    Cotter, J., Dowd, K.: Extreme spectral risk measures: an application to futures clearinghouse margin requirements. J. Bank. Finance 30, 3469–3485 (2006)CrossRefGoogle Scholar
  4. 4.
    Javidi, A.A.: Entropic value-at-risk: a new coherent risk measure. J. Optim. Theory Appl. 155, 1105–1123 (2012)MathSciNetCrossRefGoogle Scholar
  5. 5.
    Jorion, P.: Value at Risk: The New Benchmark for Managing Financial Risk. McGraw-Hill, New York (2006)Google Scholar
  6. 6.
    Markowitz, H.: Mean-Variance Analysis in Portfolio Choice and Capital Markets. Blackwell, Oxford (1990)zbMATHGoogle Scholar
  7. 7.
    Meucci, A.: Risk and Asset Allocation. Springer, Heidelberg (2005). Scholar
  8. 8.
    Pliska, S.R.: Introduction to Mathematical Finance: Discrete-Time Models. Blackwell Publisher, New York (1997)Google Scholar
  9. 9.
    Rockafellar, R.T., Uryasev, S.: Optimization of conditional value-at-risk. J. Risk 2, 21–41 (2000)CrossRefGoogle Scholar
  10. 10.
    Ross, S.M.: An Introduction to Mathematical Finance. Cambridge University Press, Cambridge (1999)zbMATHGoogle Scholar
  11. 11.
    Steinbach, M.C.: Markowitz revisited: mean-variance model in financial portfolio analysis. SIAM Rev. 43, 31–85 (2001)MathSciNetCrossRefGoogle Scholar
  12. 12.
    Tasche, D.: Expected shortfall and beyond. J. Bank. Finance 26, 1519–1533 (2002)CrossRefGoogle Scholar
  13. 13.
    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
  14. 14.
    Yoshida, Y.: A dynamic risk allocation of value-at-risks with portfolios. J. Adv. Comput. Intell. Intell. Inform. 16, 800–806 (2012)CrossRefGoogle 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
  16. 16.
    Yoshida, Y.: An optimal process for average value-at-risk portfolios in financial management. In: Ntalianis, K., Croitoru, A. (eds.) APSAC 2017. LNEE, vol. 428, pp. 101–107. Springer, Cham (2018). Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

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

Personalised recommendations