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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)

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, Jan Obłój, Peter Spoida, Nizar And, Touzi
- 2016

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)

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)

We generalize the algorithm for semi-linear parabolic PDEs in Henry-Labordère [11] to the non-Markovian case for a class of Backward SDEs (BSDEs). By simulating the branching process, the algorithm does not need any backward regression. To prove that the numerical algorithm converges to the solution of BSDEs, we use the notion of viscosity solution of path… (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]. Further, by suitable adaptation of the notion of cyclical mono-tonicity, [4] obtained an extension of the one-dimensional Brenier's theorem to the present martingale version.… (More)

VIX options traded on the CBOE have become popular volatility derivatives. As S&P 500 vanilla options and VIX both depend on S&P 500 volatility dynamics, it is important to understand the link between these products. In this paper, we bound VIX options from vanilla options and VIX futures. This leads us to introduce a new martingale optimal transportation… (More)

We develop a weak exact simulation technique for a process X defined by a multi-dimensional stochastic differential equation (SDE). Namely, for a Lipschitz function g, we propose a simulation based approximation of the expectation E[g(X t 1 , · · · , X tn)], which bypasses the discretization error. The main idea is to start instead from a well-chosen… (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)

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