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Rapport Année : 2012

Maximum Maximum of Martingales given Marginals

Résumé

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. The dual formulation converts this problem into a continuous-time martingale optimal transportation problem which we solve explicitly for Lookback options with nondecreasing payoff function. In particular, our methodology recovers the extensions of the Azéma-Yor solution of the Skorohod embedding problem obtained by Hobson and Klimmek (under slightly different conditions), those derived by Brown, Hobson and Rogers, and those obtained by Madan and Yor.
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Dates et versions

hal-00684005 , version 1 (30-03-2012)
hal-00684005 , version 2 (09-04-2013)

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Pierre Henry-Labordere, Nizar Touzi. Maximum Maximum of Martingales given Marginals. 2012. ⟨hal-00684005v1⟩
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