Convex Duality with Transaction Costs

Yan Dolinsky () and H. Mete Soner ()
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Yan Dolinsky: Department of Statistics, Hebrew University of Jerusalem, Jerusalem 91905, Israel
H. Mete Soner: Department of Mathematics, ETH Zurich, 8092 Zurich, Switzerland; Swiss Finance Institute, 8006 Zurich, Switzerland

Mathematics of Operations Research, 2017, vol. 42, issue 2, 448-471

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.

Keywords: European options; model-free hedging; semi-static hedging; transaction costs; conditional full support (search for similar items in EconPapers)
Date: 2017
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Citations: View citations in EconPapers (4)

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