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Minimax theorems for American options in incomplete markets without time-consistency

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  • Denis Belomestny
  • Volker Kraetschmer

Abstract

In this paper we give sufficient conditions guaranteeing the validity of the well-known minimax theorem for the lower Snell envelope with respect to a family of absolutely continuous probability measures. Such minimax results play an important role in the characterisation of arbitrage-free prices of American contingent claims in incomplete markets. Our conditions do not rely on the notions of stability under pasting or time-consistency and reveal some unexpected connection between the minimax result and the path properties of the corresponding density process.

Suggested Citation

  • Denis Belomestny & Volker Kraetschmer, 2017. "Minimax theorems for American options in incomplete markets without time-consistency," Papers 1708.08904, arXiv.org.
    • Handle: RePEc:arx:papers:1708.08904
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    References listed on IDEAS

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    1. Amarante, Massimiliano, 2014. "A characterization of exact non-atomic market games," Journal of Mathematical Economics, Elsevier, vol. 54(C), pages 59-62.
    2. Denis Belomestny & Volker Kraetschmer, 2014. "Optimal stopping under model uncertainty: randomized stopping times approach," Papers 1405.2240, arXiv.org, revised Dec 2014.
    3. Erhan Bayraktar & Song Yao, 2009. "Optimal Stopping for Non-linear Expectations," Papers 0905.3601, arXiv.org, revised Jan 2011.
    4. Bayraktar, Erhan & Yao, Song, 2011. "Optimal stopping for non-linear expectations--Part I," Stochastic Processes and their Applications, Elsevier, vol. 121(2), pages 185-211, February.
    5. Ioannis Karatzas & (*), S. G. Kou, 1998. "Hedging American contingent claims with constrained portfolios," Finance and Stochastics, Springer, vol. 2(3), pages 215-258.
    6. Charalambos D. Aliprantis & Kim C. Border, 2006. "Infinite Dimensional Analysis," Springer Books, Springer, edition 0, number 978-3-540-29587-7, January.
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