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Article Dans Une Revue Stochastic Processes and their Applications Année : 2016

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

Résumé

We provide an extension of the martingale version of the Fréchet-Hoeffding coupling to the infinitely-many marginals constraints setting. 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 functions and requires some restrictions on the marginal distributions. We show that the optimal martingale transference plan is induced by a pure downward jump local Lévy model. In particular, this provides a new martingale peacock process (PCOC " Processus Croissant pour l'Ordre Convexe, " see Hirsch, Profeta, Roynette & Yor [43]), and a new remarkable example of discontinuous fake Brownian motions. Further, as in [40], we also provide a duality result together with the corresponding dual optimizer in explicit form. As an application to financial mathematics, our results give the model-independent optimal lower and upper bounds for variance swaps.
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Dates et versions

hal-01429547 , version 1 (08-01-2017)

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  • HAL Id : hal-01429547 , version 1

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Pierre Henry-Labordère, Xiaolu Tan, Nizar Touzi. An Explicit Martingale Version of the One-dimensional Brenier's Theorem with Full Marginals Constraint . Stochastic Processes and their Applications, 2016. ⟨hal-01429547⟩
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