Bi-Criteria Portfolio Optimization Models with Percentile and Symmetric Risk Measures by Mathematical Programming

作者：Sawik Bartosz^*

来源：Przeglad Elektrotechniczny, 2012, 88(10B): 176-180.

• multi-criteria decision making
• portfolio optimization
• percentile and symmetric risk measures
• weighting approach
• mathematical programming

The purpose of this paper is to compare three different bi-criteria portfolio optimization models. The first model is constructed with the use of percentile risk measure Value-at-Risk and solved by mixed integer programming. The second one is constructed with the use of percentile risk measure Conditional Value-at-Risk and solved by linear programming. The third one is constructed with the use of a symmetric measure of risk - variance of return - as in the Markowitz portfolio and solved by quadratic programming. Computational experiments are conducted for bi-criteria portfolio stock exchange investments. The results obtained prove, that the bi-objective portfolio optimization models with Value-at-Risk and Conditional Value-at-Risk could be used to shape the distribution of portfolio returns. The decision maker can assess the value of portfolio return and the risk level, and can decide how to invest in a real life situation comparing with ideal (optimal) portfolio solutions. The proposed scenario-based portfolio optimization problems under uncertainty, formulated as a bi-objective linear, mixed integer or quadratic program are solved using commercially available software (AMPL/CPLEX) for mathematical programming.

• 出版日期2012