Verbesserung von Risikoschranken unter Abhängigkeitsinformation

In the project VeRAin, new methods are developed to improve risk bounds for sums of random variables under dependence information. As a basic problem, higher-dimensional dependencies cannot be determined in practice due to the curse of dimensionality and therefore the distribution of the sum cannot be obtained. The aim is to improve the worst-case bounds for important distributional quantities, such as the average value-at-risk, using easily accessible dependence information, such as correlations. To this end, new mathematical methods are researched in the area of stochastic orders and the theory of optimal transport. The results are used, for example, in finance and insurance, where extreme events for random sums need to be quantified in order to be able to make reliable decisions when weighing up risks.