Conditional dominance criteria: definition and application to risk-management

We define the concept of conditional dominance and use it for obtaining bounds on the hedging prices of random variables. These bounds depend only on the characteristics of the financial market and the random variables to hedge. Moreover, they are coherent with the equilibrium and tighter than the ones obtained by the classical super-replication approach, significantly in some cases. This approach can be applied in static as well as dynamic frameworks.