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Convex duality with transaction costs

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

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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

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