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On Shortfall Risk Minimization for Game Options

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  • Yan Dolinsky

Abstract

In this paper we study the existence of an optimal hedging strategy for the shortfall risk measure in the game options setup. We consider the continuous time Black--Scholes (BS) model. Our first result says that in the case where the game contingent claim (GCC) can be exercised only on a finite set of times, there exists an optimal strategy. Our second and main result is an example which demonstrates that for the case where the GCC can be stopped on the all time interval, optimal portfolio strategies need not always exist.

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  • Yan Dolinsky, 2020. "On Shortfall Risk Minimization for Game Options," Papers 2002.01528, arXiv.org.
    • Handle: RePEc:arx:papers:2002.01528
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    References listed on IDEAS

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    1. Miklós Rásonyi & Andrea Rodrigues, 2013. "Optimal portfolio choice for a behavioural investor in continuous-time markets," Annals of Finance, Springer, vol. 9(2), pages 291-318, May.
    2. Andreas Kyprianou, 2004. "Some calculations for Israeli options," Finance and Stochastics, Springer, vol. 8(1), pages 73-86, January.
    3. Jan Kallsen & Christoph Kühn, 2004. "Pricing derivatives of American and game type in incomplete markets," Finance and Stochastics, Springer, vol. 8(2), pages 261-284, May.
    4. Miklos Rasonyi & Andrea M. Rodrigues, 2012. "Optimal Portfolio Choice for a Behavioural Investor in Continuous-Time Markets," Papers 1202.0628, arXiv.org, revised Apr 2013.
    5. Yoshio Ohtsubo, 1986. "Optimal Stopping in Sequential Games With or Without a Constraint of Always Terminating," Mathematics of Operations Research, INFORMS, vol. 11(4), pages 591-607, November.
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