Skip to main content
SpringerLink
Log in

Time Consistent Multi-period Worst-Case Risk Measure in Robust Portfolio Selection

  • Published:
Journal of the Operations Research Society of China Aims and scope Submit manuscript

Abstract

In this paper, we first construct a time consistent multi-period worst-case risk measure, which measures the dynamic investment risk period-wise from a distributionally robust perspective. Under the usually adopted uncertainty set, we derive the explicit optimal investment strategy for the multi-period robust portfolio selection problem under the multi-period worst-case risk measure. Empirical results demonstrate that the portfolio selection model under the proposed risk measure is a good complement to existing multi-period robust portfolio selection models using the adjustable robust approach.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3

Similar content being viewed by others

Notes

  1. http://finance.yahoo.com.

References

  1. Scarf, H.: A min-max solution of an inventory problem. In: Arrow, K.J., Karlin, S., Scarf, H.E. (eds.) Studies in the Mathematical Theory of Inventory and Production, pp. 201–209. Stanford University Press, Stanford (1958)

    Google Scholar 

  2. Žácková, J.: On minimax solutions of stochastic linear programming problems. Čas. Pěst. Mat. 91, 423–430 (1966)

    MathSciNet  MATH  Google Scholar 

  3. Lobo, M., Boyd, S.: The worst-case risk of a portfolio. Technical Report, Stanford University (2000)

  4. El Ghaoui, L., Oks, M., Oustry, F.: Worst-case value-at-risk and robust portfolio optimization: a conic programming approach. Oper. Res. 51(4), 543–556 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  5. Chen, L., He, S., Zhang, S.: Tight bounds for some risk measures, with applications to robust portfolio selection. Oper. Res. 59(4), 847–865 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  6. Zhu, S., Fukushima, M.: Worst-case conditional value-at-risk with application to robust portfolio management. Oper. Res. 57(5), 1155–1168 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  7. Chen, Z., Consigli, G., Liu, J., Li, G., Fu, T., Hu, Q.: Multi-period risk measures and optimal investment policies. In: Consigli, G., Kuhn, D., Brandimarte, P. (eds.) Optimal Financial Decision Making Under Uncertainty, pp. 1–34. Springer, New York (2017a)

    Google Scholar 

  8. Li, D., Ng, W.: Optimal dynamic portfolio selection: multi-period mean-variance formulation. Math. Finance 10, 387–406 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  9. Zhu, S., Li, D., Wang, S.: Risk control over bankruptcy in dynamic portfolio selection: a generalized mean-variance formulation. IEEE Autom. Control 49, 447–457 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  10. Chen, Z., Liu, J., Li, G., Yan, Z.: Composite time consistent multi-period risk measure and its application in optimal portfolio selection. TOP 24(3), 515–540 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  11. Chen, Z., Liu, J., Hui, Y.: Recursive risk measures under regime switching applied to portfolio selection. Quant. Finance 17(9), 1457–1476 (2017b)

  12. Ben-Tal, A., El Ghaoui, L., Nemirovski, A.: Robust Optimization. Princeton University Press, Princeton, NJ (2009)

    Book  MATH  Google Scholar 

  13. Shapiro, A.: A dynamic programming approach to adjustable robust optimization. Oper. Res. Lett. 39, 83–87 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  14. Shapiro, A.: On a time consistency concept in risk averse multistage stochastic programming. Oper. Res. Lett. 37, 143–147 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  15. Wang, T.: A class of dynamic risk measure. Technical Report, University of British Columbia (1999)

  16. Weber, S.: Distribution-invariant risk measures, information, and dynamic consistency. Math. Finance 16, 419–441 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  17. Chen, Z., Li, G., Guo, J.: Optimal investment policy in the time consistent mean-variance formulation. Insur. Math. Econ. 52, 145–156 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  18. Artzner, P., Delbaen, F., Eber, J. M., Heath, D.: Coherent measures of risk. Math. Finance 9(3), 203–228 (1999)

  19. Gulpinar, N., Rustem, B.: Worst-case robust decisions for multi-period mean-variance portfolio optimization. Eur. J. Oper. Res. 183, 981–1000 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  20. Ruszczyński, A.: Risk-averse dynamic programming for markov decision processes. Math. Program. Ser. B 125, 235–261 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  21. Pflug, G., Römisch, W.: Modeling, Measuring and Managing Risk. World Scientific, Singapore (2007)

    Book  MATH  Google Scholar 

  22. Kovacevic, R., Pflug, G.: Time consistency and information monotonicity of multiperiod acceptability functionals. Radon Ser. Comp. Appl. Math. 8, 1–24 (2009)

    MathSciNet  MATH  Google Scholar 

  23. Artzner, P., Delbaen, F., Eber, J.M., Heath, D., Ku, H.: Coherent multi-period risk adjusted values and Bellman’s principle. Ann. Oper. Res. 152, 5–22 (2007)

  24. Ermoliev, Y., Gaivoronski, A., Nedeva, C.: Stochastic optimization problems with incomplete information on distribution functions. SIAM J. Control Optim. 23(5), 697–716 (1985)

    Article  MathSciNet  MATH  Google Scholar 

  25. Natarajan, K., Sim, M., Uichanco, J.: Tractable robust expected utility and risk models for portfolio optimization. Math. Finance 20(4), 695–731 (2010)

Download references

Author information

Authors and Affiliations

  1. Department of Computing Science, School of Mathematics and Statistics, Xi’an Jiaotong University, Xi’an, 710049, China

    Jia Liu, Zhi-Ping Chen & Yong-Chang Hui

Authors
  1. Jia Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Zhi-Ping Chen
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Yong-Chang Hui
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Zhi-Ping Chen.

Additional information

This paper is dedicated to Professor Duan Li in celebration of his 65th birthday.

This research was supported by the National Natural Science Foundation of China (Nos. 71371152 and 11571270)

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Liu, J., Chen, ZP. & Hui, YC. Time Consistent Multi-period Worst-Case Risk Measure in Robust Portfolio Selection. J. Oper. Res. Soc. China 6, 139–158 (2018). https://doi.org/10.1007/s40305-017-0188-9

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s40305-017-0188-9

Keywords

Mathematical Subject Classification

Search

Navigation