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Applications of weak convergence for hedging of game options

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  • Yan Dolinsky

Abstract

In this paper we consider Dynkin's games with payoffs which are functions of an underlying process. Assuming extended weak convergence of underlying processes $\{S^{(n)}\}_{n=0}^{\infty}$ to a limit process $S$ we prove convergence Dynkin's games values corresponding to $\{S^{(n)}\}_{n=0}^{\infty}$ to the Dynkin's game value corresponding to $S$. We use these results to approximate game options prices with path dependent payoffs in continuous time models by a sequence of game options prices in discrete time models which can be calculated by dynamical programming algorithms. In comparison to previous papers we work under more general convergence of underlying processes, as well as weaker conditions on the payoffs.

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  • Yan Dolinsky, 2009. "Applications of weak convergence for hedging of game options," Papers 0908.3661, arXiv.org, revised Nov 2010.
    • Handle: RePEc:arx:papers:0908.3661
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    References listed on IDEAS

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    1. Damien Lamberton, 1993. "Convergence of the Critical Price In the Approximation of American Options," Mathematical Finance, Wiley Blackwell, vol. 3(2), pages 179-190, April.
    2. Maurizio Pratelli & Sabrina Mulinacci, 1998. "Functional convergence of Snell envelopes: Applications to American options approximations," Finance and Stochastics, Springer, vol. 2(3), pages 311-327.
    3. Huisman, K.J.M., 2000. "Technology investment : A game theoretic real options approach," Other publications TiSEM f35e7474-93d7-4140-8614-f, Tilburg University, School of Economics and Management.
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    Cited by:

    1. Yuri Kifer, 2020. "Error estimates for discrete approximations of game options with multivariate diffusion asset prices," Papers 2012.01257, arXiv.org, revised Dec 2021.

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