The problern of finding the bounds on exotic derivatives prices given Vanilla ones is formulated as a super-hedging problem. The dual formulation reduces to an original optimal transportation problem which is suitable for numerical implementation. ln the context of Lookback options, standard stochastic control techniques lead to explicit solutions generalizing previous results related to the Azema-Yor solution of the Skorohod Embedding Problem. Finally, a similar approach can be developed in the context of the optimal investment problem.

Referent: Prof. Dr. Nizar Touzi, Ecole Polytechnique, Palaiseau