A Short Proof of Strassen’s Theorem Using Convex Analysis

We give a simple proof of Strassen’s theorem on stochastic dominance using linear programming duality, without requiring measure-theoretic arguments. The result extends to generalized inequalities using conic optimization duality and provides an additional, intuitive optimization formulation for stochastic dominance. Citation Northwestern Univ., Aug., 2013 Article Download View A Short Proof of Strassen's Theorem Using Convex … Read more

Decision Making under Uncertainty when Preference Information is Incomplete

We consider the problem of optimal decision making under uncertainty but assume that the decision maker’s utility function is not completely known. Instead, we consider all the utilities that meet some criteria, such as preferring certain lotteries over certain other lotteries and being risk averse, s-shaped, or prudent. This extends the notion of stochastic dominance. … Read more

Concepts and Applications of Stochastically Weighted Stochastic Dominance

Stochastic dominance theory provides tools to compare random entities. When comparing random vectors (say X and Y ), the problem can be viewed as one of multi-criterion decision making under uncertainty. One approach is to compare weighted sums of the components of these random vectors using univariate dominance. In this paper we propose new concepts … Read more

Models and Formulations for Multivariate Dominance Constrained Stochastic Programs

Dentcheva and Ruszczynski recently proposed using a stochastic dominance constraint to specify risk preferences in a stochastic program. Such a constraint requires the random outcome resulting from one’s decision to stochastically dominate a given random comparator. These ideas have been extended to problems with multiple random outcomes, using the notion of positive linear stochastic dominance. … Read more

Risk Adjusted Budget Allocation Models with Application in Homeland Security

This paper presents and studies several models for multi-criterion budget allocation problems under uncertainty. We start by introducing a robust weighted objective model, which is developed further using the concept of stochastic dominance to incorporate risk averseness of the decision maker. A budget minimization variant of this model is also presented. We use a Sample … Read more

Sample Average Approximation for Stochastic Dominance Constrained Programs

In this paper we study optimization problems with second-order stochastic dominance constraints. This class of problems has been receiving increasing attention in the literature as it allows for the modeling of optimization problems where a risk-averse decision maker wants to ensure that the solution produced by the model dominates certain benchmarks. Here we deal with … Read more

Asset-Liability Management Modelling with Risk Control by Stochastic Dominance

An Asset-Liability Management model with a novel strategy for controlling risk of underfunding is presented in this paper. The basic model involves multiperiod decisions (portfolio rebalancing) and deals with the usual uncertainty of investment returns and future liabilities. Therefore it is well-suited to a stochastic programming approach. A stochastic dominance concept is applied to measure … Read more

A Cutting Surface Method for Uncertain Linear Programs with Polyhedral Stochastic Dominance Constraints

In this paper we study linear optimization problems with multi-dimensional linear positive second-order stochastic dominance constraints. By using the polyhedral properties of the second- order linear dominance condition we present a cutting-surface algorithm, and show its finite convergence. The cut generation problem is a difference of convex functions (DC) optimization problem. We exploit the polyhedral … Read more

Valid Inequalities and Restrictions for Stochastic Programming Problems with First Order Stochastic Dominance Constraints

Stochastic dominance relations are well-studied in statistics, decision theory and economics. Recently, there has been significant interest in introducing dominance relations into stochastic optimization problems as constraints. In the discrete case, stochastic optimization models involving second order stochastic dominance (SSD) constraints can be solved by linear programming (LP). However, problems involving first order stochastic dominance … Read more

Convexification of Stochastic Ordering

We consider sets defined by the usual stochastic ordering relation and by the second order stochastic dominance relation. Under fairy general assumptions we prove that in the space of integrable random variables the closed convex hull of the first set is equal to the second set. Article Download View Convexification of Stochastic Ordering