# Convex duality with transaction costs

## Author(s): Dolinsky, Y; Soner, H Mete

To refer to this page use: http://arks.princeton.edu/ark:/88435/pr1mk3m
 Abstract: © 2016 INFORMS. 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. Publication Date: 1-May-2017 Citation: Dolinsky, Y, Mete Soner, H. (2017). Convex duality with transaction costs. Mathematics of Operations Research, 42 (2), 448 - 471. doi:10.1287/moor.2016.0811 DOI: doi:10.1287/moor.2016.0811 ISSN: 0364-765X EISSN: 1526-5471 Pages: 448 - 471 Type of Material: Journal Article Journal/Proceeding Title: Mathematics of Operations Research Version: Author's manuscript