### 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 | English (US) |
---|---|

Pages (from-to) | 448-471 |

Number of pages | 24 |

Journal | Mathematics of Operations Research |

Volume | 42 |

Issue number | 2 |

DOIs | |

State | Published - May 2017 |

Externally published | Yes |

### All Science Journal Classification (ASJC) codes

- Mathematics(all)
- Computer Science Applications
- Management Science and Operations Research

### Keywords

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

## Fingerprint Dive into the research topics of 'Convex duality with transaction costs'. Together they form a unique fingerprint.

## Cite this

*Mathematics of Operations Research*,

*42*(2), 448-471. https://doi.org/10.1287/moor.2016.0811