An Explicit Martingale Version of Brenier's Theorem

An Explicit Martingale Version of Brenier’s Theorem

By investigating model-independent bounds for exotic options in financial mathematics, a martingale version of the Monge-Kantorovich mass transport problem was introduced in [3, 24]. In this paper, we extend the one-dimensional Brenier’s theorem to the present martingale version. We provide the explicit martingale optimal transference plans for a remarkable class of coupling functions correspon...

An explicit martingale version of the one-dimensional Brenier theorem

By investigating model-independent bounds for exotic options in financial mathematics, a martingale version of the Monge-Kantorovich mass transport problem was introduced in [3, 24]. Further, by suitable adaptation of the notion of cyclical monotonicity, [4] obtained an extension of the one-dimensional Brenier’s theorem to the present martingale version. In this paper, we complement the previou...

An Explicit Martingale Version of the One - dimensional Brenier ’ s Theorem with Full Marginals Constraint ∗

We provide an extension to the infinitely-many marginals case of the martingale version of the Fréchet-Hoeffding coupling (which corresponds to the one-dimensional Brenier theorem). In the two-marginal context, this extension was obtained by Beiglböck & Juillet [7], and further developed by Henry-Labordère & Touzi [40], see also [6]. Our main result applies to a special class of reward function...

A Purely Martingale Version of Lindeberg's Central Limit Theorem

A Martingale Decomposition Theorem