In optimization problems appearing in fields such as economics, finance, or engineering, it is often important that a risk measure of a decision-dependent random variable stays below a prescribed level. At the same time, the underlying probability distribution determining the risk measure’s value is typically known only up to a certain degree and the constraint … Read more
Motivated by situations in which independent agents, or players, wish to cooperate in some uncertain endeavor over time, we study dynamic linear programming games, which generalize classical linear production games to multi-period settings under uncertainty. We specifically consider that players may have risk-averse attitudes towards uncertainty, and model this risk aversion using coherent conditional risk … Read more
Abstract In this paper we discuss continuity properties of acceptability functionals or risk measures. The dependence of the random variable is investigated first. The main contribution and focus of this paper is to study how acceptability functionals vary whenever the underlying probability measure is perturbed. Abstract It turns out that the Wasserstein distance provides a … Read more