Marginal and Dependence Uncertainty: Bounds, Optimal Transport, And Sharpness

Motivated by applications in model-free finance and quantitative risk management, we consider Frechet classes of multivariate distribution functions where additional information on the joint distribution is assumed, while uncertainty in the marginals is also possible. We derive optimal transport duality results for these Frechet classes that...

Weak and Strong Type A 1 –A ∞ Estimates for Sparsely Dominated Operators

We consider operators T satisfying a sparse domination property (Formula presented.)with averaging exponents (Formula presented.). We prove weighted strong type boundedness for (Formula presented.) and use new techniques to prove weighted weak type (Formula presented.) boundedness with quantitative mixed (Formula presented.)–(Formula...