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We consider the problem of superhedging under volatility uncertainty for an investor allowed to dynamically trade the underlying asset, and statically trade European call options for all possible strikes with some given maturity. This problem is classically approached by means of the Skorohod Embedding Problem (SEP). Instead, we provide a dual formulation… (More)

In this paper we investigate model-independent bounds for exotic options written on a risky asset using infinite-dimensional linear programming methods. Based on arguments from the theory of Monge-Kantorovich mass-transport we establish a dual version of the problem that has a natural financial interpretation in terms of semi-static hedging. In particular… (More)

A survey of ideas, techniques and results from d=5 supergravity for the conformal and mass-perturbed phases of d=4 N =4 Super-Yang-Mills theory.

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 Bei-glböck & Juillet [7], and further developed by Henry-Labordère & Touzi [40], see also [6]. Our main result… (More)

- Pierre Henry-Labordère, Bernard Julia, Louis Paulot
- 2002

It is well known but rather mysterious that root spaces of the E n Lie groups appear in the second integral cohomology of regular, complex, compact, del Pezzo surfaces. The corresponding groups act on the scalar fields (0-forms) of toroidal compactifications of M theory. Their Borel subgroups are actually subgroups of supergroups of finite dimension over… (More)

- Pierre Henry-Labordère, Jan Ob, Peter Spoida, Nizar Touzi
- 2013

We consider the problem of superhedging under volatility uncertainty for an investor allowed to dynamically trade the underlying asset and statically trade European call options for all possible strikes and finitely-many maturities. We present a general du-ality result which converts this problem into a min-max calculus of variations problem where the… (More)

- Pierre Henry-Labordère, Jan Obłój, Peter Spoida, Nizar And, Touzi
- 2014

We obtain bounds on the distribution of the maximum of a martingale with fixed marginals at finitely many intermediate times. The bounds are sharp and attained by a solution to n-marginal Skorokhod embedding problem in Obłój and Spoida [An iterated Azéma-Yor type embedding for finitely many marginals (2013) Preprint]. It follows that their embedding… (More)

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 transfer-ence plans for a… (More)

- Pierre Henry-Labordère, Bernard Julia, Louis Paulot
- 2003

The correspondence between del Pezzo surfaces and field theory models, discussed in [1] and in [2] over the complex numbers or for split real forms, is extended to other real forms, in particular to those compatible with supersymmetry. Specifically, all theories of the Magic triangle [3] that reduce to the pure supergravities in four dimensions correspond… (More)

We show that the left-monotone martingale coupling is optimal for any given performance function satisfying the martingale version of the Spence-Mirrlees condition, without assuming additional structural conditions on the marginals. We also give a new interpretation of the left monotone coupling in terms of Skorokhod embedding which allows us to give a… (More)