Multiperiod Mean-CVaR Portfolio Selection

  • Xiangyu CuiEmail author
  • Yun Shi
Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 359)


Due to the time inconsistency issue of multiperiod mean-CVaR model, two important policies of the model with finite states, the pre-committed policy and the time consistent policy, are derived and discussed. The pre-committed policy, which is global optimal for the model, is solved through linear programming. A detailed analysis shows that the pre-committed policy doesn’t satisfy time consistency in efficiency either, i.e., the truncated pre-committed policy is not efficient for the remaining short term mean-CVaR problem. The time consistent policy, which is the subgame Nash equilibrium policy of the multiperson game reformulation of the model, takes a piecewise linear form of the current wealth level and the coefficients can be derived by a series of integer programming problems and two linear programming problems. The difference between two polices indicates the degree of time inconsistency.


mean-CVaR pre-committed policy time consistency in efficiency time consistent policy linear programming integer programming 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Artzner, P., Delbaen, F., Eber, J.M., Heath, D.: Coherent measures of risk. Mathematical Finance 4, 203–228 (1999)CrossRefMathSciNetGoogle Scholar
  2. 2.
    Artzner, P., Delbaen, F., Eber, J.M., Heath, D., Ku, H.: Coherent multiperiod risk adjusted values and Bellman’s principle. Annals of Operations Research 152, 5–22 (2007)CrossRefzbMATHMathSciNetGoogle Scholar
  3. 3.
    Basak, S., Chabakauri, G.: Dynamic mean-variance asset allocation. Review of Financial Studies 23, 2970–3016 (2010)CrossRefGoogle Scholar
  4. 4.
    Björk, T., Murgoci, A.: A general theory of Markovian time inconsistent stochasitc control problem, working paper (2010)Google Scholar
  5. 5.
    Björk, T., Murgoci, A., Zhou, X.Y.: Mean-variance portfolio optimization with state dependent risk aversion. Mathematical Finance 24, 1–24 (2014)CrossRefzbMATHMathSciNetGoogle Scholar
  6. 6.
    Boda, K., Filar, J.A.: Time consistent dynamic risk measures. Mathematical Methods of Operations Reseach 63, 169–186 (2006)CrossRefzbMATHMathSciNetGoogle Scholar
  7. 7.
    Cui, X.Y., Li, D., Wang, S.Y., Zhu, S.S.: Better Than Dynamic Mean-Variance: Time Inconsistency and Free Cash Flow Stream. Mathematical Finance 22, 346–378 (2012)CrossRefzbMATHMathSciNetGoogle Scholar
  8. 8.
    Gao, J.J., Zhou, K., Li, D., Cao, X.R.: Dynamic Mean-LPM and Mean-CVaR Portfolio Optimization in Continuous-time, working paper, arXiv:1402.3464 (2014)Google Scholar
  9. 9.
    Rockafellar, T.R., Uryasev, S.P.: Optimization of Conditional Value-at-Risk. Journal of Risk 2, 21–41 (2000)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.School of Statistics and ManagementShanghai University of Finance and EconomicsShanghaiChina
  2. 2.School of ManagementShanghai UniversityShanghaiChina

Personalised recommendations