## Abstract

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 with some given maturity. This problem is classically approached by means of the Skorohod Embedding Problem (sep). Instead, we provide a dual formulation which converts the superhedging problem into a continuous martingale optimal transportation problem. We then show that this formulation allows us to recover previously known results about lookback options. In particular, our methodology induces a new proof of the optimality of Azéma-Yor solution of the sep for a certain class of lookback options. Unlike the sep technique, our approach applies to a large class of exotics and is suitable for numerical approximation techniques.

Original language | English (US) |
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Pages (from-to) | 312-336 |

Number of pages | 25 |

Journal | Annals of Applied Probability |

Volume | 24 |

Issue number | 1 |

DOIs | |

State | Published - Feb 2014 |

## Keywords

- Convex duality
- Optimal control
- Volatility uncertainty

## ASJC Scopus subject areas

- Statistics and Probability
- Statistics, Probability and Uncertainty