Maximum Maximum of Martingales given Marginals

Details Maximum Maximum of Martingales given Marginals Maximum Maximum of Martingales given Marginals

2012-03-30

arxiv.org/abs/1203.6877v1

Mathematics

Probability

Scientific paper

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 Az\'ema-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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