Revenue and Cost Uncertainty, Generalized Mean‐Variance, and the Linear Complementarity Problem

Symmetric quadratic programming and the linear complementarity problem are presented in the context of a novel interpretation of risk programming. The novelty admits stochastic supplies of limiting inputs, and yet it preserves the linearity of the structural constraints. This formulation is, therefore, a generalization of the traditional mean‐variance approach originated with Markowitz's portfolio analysis and extended by Freund to farm planning under uncertain revenues. The specification admits also nonzero covariances between revenues and costs of limiting inputs and allows the computation of risk coefficients associated with a companion chance‐constrained problem.