American options with gradual exercise under proportional transaction costs

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American options in a multi-asset market model with proportional transaction costs are studied in the case when the holder of an option is able to exercise it gradually at a so-called mixed (randomized) stopping time. The introduction of gradual exercise leads to tighter bounds on the option price when compared to the case studied in the existing literature, where the standard assumption is that the option can only be exercised instantly at an ordinary stopping time. Algorithmic constructions for the bid and ask prices and the associated superhedging strategies and optimal mixed stopping times for an American option with gradual exercise are developed and implemented, and dual representations are established.
Original languageEnglish
Article number1450052
Number of pages36
JournalInternational Journal of Theoretical and Applied Finance
Issue number8
Early online date26 Dec 2014
Publication statusPublished - Dec 2014

Bibliographical note

© World Scientific Publishing Co. This is an author produced version of a paper published in International Journal of Theoretical and Applied Finance. Uploaded in accordance with the publisher's self-archiving policy.


  • American options
  • transaction costs
  • mixed stopping times
  • superhedging
  • dual representation

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