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# Applications of weak convergence for hedging of game options

Listed:
• 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.

## Suggested Citation

• 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
as

File URL: http://arxiv.org/pdf/0908.3661

## References listed on IDEAS

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1. 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.
2. Damien Lamberton, 1993. "Convergence of the Critical Price In the Approximation of American Options," Mathematical Finance, Wiley Blackwell, vol. 3(2), pages 179-190.
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