Pierre Henry-Labordère

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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 MongeKantorovich mass-transport we establish a dual version of the problem that has a natural financial interpretation in terms of semi-static hedging. In particular we(More)
We obtain bounds on the distribution of the maximum of a continuous 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 Ob lój & Spoida [44]. It follows that their embedding maximises the maximum among all other embeddings. Our motivating problem is(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 transference plans for a remarkable(More)
The purpose of this paper is to design an algorithm for the computation of the counterparty risk which is competitive in regards of a brute force “Monte-Carlo of Monte-Carlo” method (with nested simulations). This is achieved using marked branching diffusions describing a Galton-Watson random tree. Such an algorithm leads at the same time to a computation(More)
We provide a representation result of parabolic semi-linear PD-Es, with polynomial nonlinearity, by branching diffusion processes. We extend the classical representation for KPP equations, introduced by Skorokhod [23], Watanabe [27] and McKean [18], by allowing for polynomial nonlinearity in the pair (u,Du), where u is the solution of the PDE with space(More)
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 duality result which converts this problem into a min-max calculus of variations problem where the(More)
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(More)