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General Duality for Perpetual American Options

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  • Aur'elien Alfonsi

    (CERMICS)

  • Benjamin Jourdain

    (CERMICS)

Abstract

In this paper, we investigate the generalization of the Call-Put duality equality obtained in [1] for perpetual American options when the Call-Put payoff $(y-x)^+$ is replaced by $\phi(x,y)$. It turns out that the duality still holds under monotonicity and concavity assumptions on $\phi$. The specific analytical form of the Call-Put payoff only makes calculations easier but is not crucial unlike in the derivation of the Call-Put duality equality for European options. Last, we give some examples for which the optimal strategy is known explicitly.

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  • Aur'elien Alfonsi & Benjamin Jourdain, 2006. "General Duality for Perpetual American Options," Papers math/0612649, arXiv.org.
    • Handle: RePEc:arx:papers:math/0612649
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    1. Aur'elien Alfonsi & Benjamin Jourdain, 2006. "A Call-Put Duality for Perpetual American Options," Papers math/0612648, arXiv.org.
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    Cited by:

    1. Hyong-chol O & Song-San Jo, 2019. "Variational inequality for perpetual American option price and convergence to the solution of the difference equation," Papers 1903.05189, arXiv.org.

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    1. Hyong-chol O & Song-San Jo, 2019. "Variational inequality for perpetual American option price and convergence to the solution of the difference equation," Papers 1903.05189, arXiv.org.
    2. Aurélien Alfonsi & Benjamin Jourdain, 2008. "General Duality For Perpetual American Options," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 11(06), pages 545-566.
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