An Explicit Martingale Version of the One-dimensional Brenier's Theorem with Full Marginals Constraint - Archive ouverte HAL Accéder directement au contenu
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.
Fichier principal
Vignette du fichier
MartingaleBrenierII.pdf (578.42 Ko) Télécharger le fichier
Origine Fichiers produits par l'(les) auteur(s)
Loading...

Dates et versions

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

Identifiants

  • HAL Id : hal-01429547 , version 1

Citer

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⟩
257 Consultations
200 Téléchargements

Partager

Gmail Mastodon Facebook X LinkedIn More