Optimal transport and hedging

Prof. Nizar Touzi (Ecole Polytechnique, Palaiseau)
Dr. Dylan Possamaï (Université Paris Dauphine)

February 27, 2013, 13:00 - 15:00, HG G 43
Nizar Touzi: Martingale optimal transport

March 13, 2013, 13:00 - 15:00, HG G 43
Nizar Touzi: Martingale optimal transport

March 20, 2013, 13:00 - 15:00, HG G 43
Dylan Possamaï: Quasi-sure hedging

March 27, 2013, 13:00 - 15:00, HG G 43
Dylan Possamaï: 2BSDEs and robust utility maximization

Abstract

The aim of these lectures is to introduce model-free formulation of robust hedging and the related second order backward SDEs problems. The first part concentrates on discrete-time models. We introduce the martingale optimal transportation problem, and the corresponding dual. Both problems have relevant interpretations in financial mathematics. We prove a general duality result. Then, we provide an extension of the Brenier theorem in the present martingale framework. The continuous-time formulation of the problem involves the theory of quasi-sure analysis, and establishes an interesting connection with the Skorohod embedding problem. The quasi sure analysis is also a key-framework for the well-posedness of second order backward SDEs. This is the main focus of the second part of the lectures where the main wellposedness results are established.