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On the Multi-Dimensional Controller and Stopper Games

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  • Erhan Bayraktar
  • Yu-Jui Huang

Abstract

We consider a zero-sum stochastic differential controller-and-stopper game in which the state process is a controlled diffusion evolving in a multi-dimensional Euclidean space. In this game, the controller affects both the drift and the volatility terms of the state process. Under appropriate conditions, we show that the game has a value and the value function is the unique viscosity solution to an obstacle problem for a Hamilton-Jacobi-Bellman equation.

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File URL: http://arxiv.org/pdf/1009.0932
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Bibliographic Info

Paper provided by arXiv.org in its series Papers with number 1009.0932.

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Date of creation: Sep 2010
Date of revision: Jan 2013
Handle: RePEc:arx:papers:1009.0932

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Web page: http://arxiv.org/

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  1. Erhan Bayraktar & Virginia Young, 2011. "Proving regularity of the minimal probability of ruin via a game of stopping and control," Finance and Stochastics, Springer, vol. 15(4), pages 785-818, December.
  2. Ioannis Karatzas & (*), S. G. Kou, 1998. "Hedging American contingent claims with constrained portfolios," Finance and Stochastics, Springer, vol. 2(3), pages 215-258.
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