Portfolio Risk Management Modelling by Bi-level Optimization

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


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.


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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© 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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