Optimization of Measures of Risk

Suppose a mapping \(F:\mathfrak {X}\to \mathcal {L}_p(\varOmega ,\mathcal {F},P)\) , where p ≥ 1, describes the dependence of a random “cost” in a stochastic system on decision variables \(x\in \mathfrak {X}\) , that is, [F(x)](ω) is the cost associated with decision x and elementary event ω ∈ Ω.