Uniform quasi‐concavity in probabilistic constrained stochastic programming

A probabilistic constrained stochastic linear programming problem is considered, where the rows of the random technology matrix are independent and normally distributed. The quasi‐concavity of the constraining function needed for the convexity of the problem is ensured if the factors of the function are uniformly quasi‐concave. 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.