## Abstract

Convex duality for two different super-replication problems in a continuous time financial market with proportional transaction cost is proved. In this market, static hedging in a finite number of options, in addition to usual dynamic hedging with the underlying stock, are allowed. The first one of the problems considered is the model-independent hedging that requires the super-replication to hold for every continuous path. In the second one the market model is given through a probability measure P and the inequalities are understood the probability measure almost surely. The main result, using the convex duality, proves that the two super-replication problems have the same value provided that the probability measure satisfies the conditional full support property. Hence, the transaction costs prevents one from using the structure of a specific model to reduce the super-replication cost.

Original language | American English |
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Pages (from-to) | 448-471 |

Number of pages | 24 |

Journal | Mathematics of Operations Research |

Volume | 42 |

Issue number | 2 |

DOIs | |

State | Published - May 2017 |

### Bibliographical note

Publisher Copyright:© 2016 INFORMS.

## Keywords

- Conditional full support
- European options
- Model-free hedging
- Semi-static hedging
- Transaction costs