We derive no-arbitrage bounds for expected excess returns to generate scenarios used in financial applications. The bounds allow to distinguish three regions: one where arbitrage opportunities will never exist, a second where arbitrage may be present, and a third, where arbitrage opportunities...

Many numerical optimization methods use scenario trees as a discrete approximation for the true (multi-dimensional) probability distributions of the problem's random variables. Realistic specifications in financial optimization models can lead to tree sizes that quickly become computationally...