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Superhedging of American options on an incomplete market with discrete time and finite horizon

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Abstract

We establish an existence criterion for the decomposition that generalizes a wellknown uniform Doob decomposition to a set of equivalent probability measures. Based on this criterion, we obtain necessary and sufficient existence conditions for a minimal superhedging (with respect to any measure out of the set of equivalent measures) American option portfolio on an incomplete frictionless market with a finite number of risky assets, discrete time, and finite horizon. We give a sample construction of such a portfolio for an American option with an arbitrary bounded dynamical contingent claim on an incomplete market with one risky asset.

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Authors and Affiliations

  1. Moscow Institute of Electronics and Mathematics, National Research University “Higher School of Economics,”, Moscow, Russia

    V. M. Khametov

  2. Central Economics and Mathematics Institute, Russian Academy of Sciences, Moscow, Russia

    E. A. Shelemekh

Authors
  1. V. M. Khametov
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  2. E. A. Shelemekh
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Correspondence to V. M. Khametov.

Additional information

Original Russian Text © V.M. Khametov, E.A. Shelemekh, 2015, published in Avtomatika i Telemekhanika, 2015, No. 9, pp. 125–149.

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Khametov, V.M., Shelemekh, E.A. Superhedging of American options on an incomplete market with discrete time and finite horizon. Autom Remote Control 76, 1616–1634 (2015). https://doi.org/10.1134/S0005117915090088

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  • DOI: https://doi.org/10.1134/S0005117915090088

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