Portfolio Risk Management Modelling by Bi-level Optimization

  • Todor Stoilov
  • Krasimira Stoilova
Part of the Intelligent Systems Reference Library book series (ISRL, volume 33)

Abstract

The portfolio optimization theory targets the optimal resource allocation between sets of securities, available at the financial markets. Thus, the investment process is a task, which targets the maximization of the portfolio return and minimization of the portfolio risk. Because such an optimization problem becomes multi-criterion optimization one it lacks an unique solution. A balance between the portfolios risk and portfolio return has to be integrated in a common scalar criterion for the risk management. The book chapter considers a bi-level optimization paradigm for the investment process. The optimization process evaluates the optimal Sharp ratio of risk versus the return to identify the parameter of the investor’s preferences to risk at the upper level. At the lower level of optimization the optimal portfolio is evaluated using the upper level defined investor’s preferences. In that manner, the portfolio optimization results in an unique solution, which is determined according to the objective considerations and it is not based on subjective assumptions of the portfolio problem. As a result, the portfolio risk is minimized according to two arguments: the content of the portfolio with appropriate assets and by the parameter of investor’s preferences to risk.

Keywords

Portfolio Optimization Efficient Frontier Sharp Ratio Level Problem Portfolio Return 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    Bodie, Z., Kane, A., Marcus, A.: Investments. Naturela, Sofia (2000)Google Scholar
  2. 2.
    Campbell, J., Chacko, G., Rodriguez, J., Viceira, L.: Strategic Asset Allocation in a Continuous-Time VAR Model, pp. 1–21. Harvard University, Cambridge (2002)Google Scholar
  3. 3.
    Christoffersen, P.F.: Elements of financial risk management. Elsevier (2003)Google Scholar
  4. 4.
    Fang, Y., Lai, K.K., Wang, S.: Fuzzy portfolio optimization. Springer, Heidelberg (2008)MATHCrossRefGoogle Scholar
  5. 5.
    Ivanova, Z., Stoilova, K., Stoilov, T.: Portfolio optimization-Internet Information Service. Academician Publisher M. Drinov, Sofia (2005) (in Bulgarian)Google Scholar
  6. 6.
    Kohlmann, M., Tang, S.: Minimization of risk and linear quadratic optimal control theory. SIAM J. Control Optim. 42, 1118–1142 (2003)MathSciNetMATHCrossRefGoogle Scholar
  7. 7.
    Korn, R.: Continuous-Time Portfolio Optimization Under Terminal Wealth Constraints. ZOP-Mathematical Methods of Operations Research 42, 69–92 (1995)MathSciNetMATHCrossRefGoogle Scholar
  8. 8.
    Magiera, P., Karbowski, A.: Dynamic portfolio optimization with expected value-variance criteria. Bucharest, 308–313 (2001)Google Scholar
  9. 9.
    Markowitz, H.M.: Portfolio selection. J. of Finance 7, 77–91 (1952)CrossRefGoogle Scholar
  10. 10.
    Mateev, M.: Analysis and assessment of investment risk. University publisher Economy, Sofia (2000) (in Bulgarian)Google Scholar
  11. 11.
    Sharpe, W., Alexander, G., Bailey, J.: Investments. Prentice Hall, England Cliffs (1999)Google Scholar
  12. 12.
    Sharpe, W.: Portfolio theory & Capital markets. Mc Grow Hill (2000)Google Scholar
  13. 13.
    Shimizu, K., Ishizuka, Y., Bard, J.: Nondifferentiable and Two-Level Mathematical Programming. Kluwer Academic Publishers (1997)Google Scholar
  14. 14.
    Simaan, M.: Stackelberg Optimization of Two-Level Systems. IEEE Trans. Systems, Man and Cybernetics, SMC 7, 554–556 (1997)MathSciNetGoogle Scholar
  15. 15.
    Simaan, M., Cruz, J.B.: On the Stackelberg Strategy in Nonzero-sum Games. J. of Optimiz. Theory & Applic. 11, 535–555 (1973)Google Scholar
  16. 16.
    Stackelberg, H.: The Theory of the Market Economy. Oxford University Press (1952)Google Scholar
  17. 17.
    Stoilov, T., Stoilova, K.: Noniterative Coordination in Multilevel Systems. Kluwer Academic Publisher, Dordrecht (1999)MATHCrossRefGoogle Scholar
  18. 18.
    Stoilova, K., Stoilov, T.: Noniterative Coordination Application in Solving Portfolio Optimisation Problems. In: Proceedings of the International Conference Automatics and Informatics, Sofia, pp. 159–162 (2003)Google Scholar
  19. 19.
    Stoilova, K.: Predictive Noniterative Coordination in Hierarchical Two-level Systems. Comptes Rendus De l’Académie Bulgare Des Sciences 58, 523–530 (2005)Google Scholar
  20. 20.
    Thomas, L.C.: A survey of credit and behavioural scoring: forecasting finan-cial risk of lending to consumers. Int. J. of Forecasting 16, 149–172 (2000)MATHCrossRefGoogle Scholar
  21. 21.
    Zadeh: Fuzzy sets. Information and Control 8, 338–353 (1965)MathSciNetMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Todor Stoilov
    • 1
  • Krasimira Stoilova
    • 1
  1. 1.Institute of Information and Communication TechnologiesBulgarian Academy of SciencesSofiaBulgaria

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