We suggest a method for equivalent transformation of a quantile optimization problem with discrete distribution of random parameters to mixed integer programming problems. The number of additional integer (in fact boolean) variables in the equivalent problems equals to the number of possible scenarios for random data. The obtained mixed integer problems are solved by standard discrete optimization software. Applications to financial portfolio optimization are considered. Results of a numerical experiment are presented.
Kibzun, A.I., Naumov, A.V., and Norkin, V.I.On reducing a quantile optimization problem with discrete distribution to a mixed integer programming problem // Automation and Remote Control. June 2013, Volume 74, Issue 6, pp 951-967