Convex duality with transaction costs

Yan Dolinsky, H. Mete Soner

Research output: Contribution to journalArticle

2 Scopus citations

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 languageEnglish (US)
Pages (from-to)448-471
Number of pages24
JournalMathematics of Operations Research
Volume42
Issue number2
DOIs
StatePublished - May 2017
Externally publishedYes

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

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