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The Duality Principle for Multidimensional Optional Semimartingales

Author

Listed:
  • Mahdieh Aminian Shahrokhabadi

    (Mathematics and Statistical Sciences Department, Faculty of Science, University of Alberta, Central Academic Building, Edmonton, AB T6G 2G1, Canada
    These authors contributed equally to this work.)

  • Alexander Melnikov

    (Mathematics and Statistical Sciences Department, Faculty of Science, University of Alberta, Central Academic Building, Edmonton, AB T6G 2G1, Canada
    These authors contributed equally to this work.)

  • Andrey Pak

    (SS&C Technologies, Toronto, ON M5V 3K2, Canada
    These authors contributed equally to this work.)

Abstract

In option pricing, we often deal with options whose payoffs depend on multiple factors such as foreign exchange rates, stocks, etc. Usually, this leads to a knowledge of the joint distributions and complicated integration procedures. This paper develops an alternative approach that converts the option pricing problem into a dual one and presents a solution to the problem in the optional semimartingale setting. The paper contains several examples which illustrate its results in terms of the parameters of models and options.

Suggested Citation

  • Mahdieh Aminian Shahrokhabadi & Alexander Melnikov & Andrey Pak, 2024. "The Duality Principle for Multidimensional Optional Semimartingales," JRFM, MDPI, vol. 17(2), pages 1-22, January.
    • Handle: RePEc:gam:jjrfmx:v:17:y:2024:i:2:p:43-:d:1326475
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    References listed on IDEAS

    as
    1. Albert N. Shiryaev & Jan Kallsen, 2002. "The cumulant process and Esscher's change of measure," Finance and Stochastics, Springer, vol. 6(4), pages 397-428.
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