Uniform quasi-concavity in probabilistic constrained stochastic programming

A probabilistic constrained stochastic programming problem is considered, where the underlying problem has linear constraints with random technology matrix. The rows of the matrix are assumed to be stochastically independent and normally distributed. For the convexity of the problem the quasi-concavity of the constraining function is needed that is ensured if the factors are uniformly quasiconcave. In the paper a necessary and sufficient condition is given for that property to hold. It is also shown, through numerical examples, that such a special problem still has practical application in optimal portfolio construction. Acknowledgements: This research was supported by National Science Foundation Grant CMMI-0856663.