In classical two-stage stochastic programming the expected value of the total costs is minimized. Recently, mean-risk models studied in mathematical finance for several decades have attracted attention in stochastic programming. We consider Conditional Value-at-Risk as risk measure in the framework of two-stage stochastic integer programming. The paper addresses structure, stability, and algori...

Let u(t; x); t 2 R; be an adapted process parametrized by a variable x in some metric space X, (!; dx) a probability kernel on the product of the probability space and the Borel sets of X. We deal with the question whether the Stratonovich integral of u(:; x) with respect to a Wiener process on and the integral of u(t; :) with respect to the random measure (:; dx) can be interchanged. This ques...

Stability analysis for optimization problems with chance constraints concerns impact of variation of probability measure in the chance constraints on the optimal value and optimal solutions and research on the topic has been well documented in the literature of stochastic programming. In this paper, we extend such analysis to optimization problems with distributionally robust chance constraints...

We consider a parametric stochastic quasi-variational inequality problem (SQVIP for short) where the underlying normal cone is defined over the solution set of a parametric stochastic cone system. We investigate the impact of variation of the probability measure and the parameter on the solution of the SQVIP. By reformulating the SQVIP as a natural equation and treating the orthogonal projectio...

We discuss a method of ranking allocations in economic environments which applies when we do not know the names or preferences of individual agents. We require that two allocations can be ranked with the knowledge only of their aggregate bundles and community indifference sets–a condition we refer to as aggregate independence. We also postulate a basic Pareto and continuity property, and a prop...

This is sometimes denoted simply “X−1(B) ⊂ F.” Since the probability measure P is only defined on sets F ∈ F, a random variable must satisfy this condition if we are to be able to find the probability Pr[X ∈ B] for each Borel set B, or even if we want to find the distribution function (DF) FX(b) ≡ Pr[X ≤ b] for each rational number b. Note that set-inverses are rather well-behaved functions fro...