Marco Frittelli

Title: Entropy Martingale Optimal Transport and Nonlinear Pricing-Hedging Duality

Abstract: We develop a duality between a novel Entropy Martingale Optimal Transport (EMOT) problem

and an associated optimization problem. In EMOT we follow the approach taken in the Entropy

Optimal Transport (EOT) problem, but we add the constraint, typical of

Martingale Optimal Transport (MOT) theory, that the infimum of the cost

functional is taken over martingale probability measures. In the associated

problem the objective functional, related via Fenchel conjugacy to the

entropic term in EMOT, is not anymore linear, as in (Martingale) Optimal Transport. This leads to a

novel optimization problem which also has a clear financial interpretation

as a nonlinear subhedging value. Our theory allows us to establish a

nonlinear robust pricing-hedging duality, which also covers a wide range of known

robust results. We also focus on Wasserstein-induced penalizations and we

study how the duality is affected by variations in the penalty terms, with a

special focus on the convergence of EMOT to the extreme case of MOT.

Joint with Alessandro Doldi