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A Dynkin game on assets with incomplete information on the return

Listed author(s):
  • De Angelis, Tiziano
  • Gensbittel, Fabien
  • Villeneuve, Stéphane

This paper studies a 2-players zero-sum Dynkin game arising from pricing an option on an asset whose rate of return is unknown to both players. Using filtering techniques we first reduce the problem to a zero-sum Dynkin game on a bi-dimensional diffusion (X; Y ). Then we characterize the existence of a Nash equilibrium in pure strategies in which each player stops at the hitting time of (X; Y ) to a set with moving boundary. A detailed description of the stopping sets for the two players is provided along with global C1 regularity of the value function.

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File URL: https://www.tse-fr.eu/sites/default/files/TSE/documents/doc/wp/2017/wp_tse_815.pdf
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Paper provided by Toulouse School of Economics (TSE) in its series TSE Working Papers with number 17-815.

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Date of creation: May 2017
Handle: RePEc:tse:wpaper:31754
Contact details of provider: Phone: (+33) 5 61 12 86 23
Web page: http://www.tse-fr.eu/

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  1. Andreas Kyprianou, 2004. "Some calculations for Israeli options," Finance and Stochastics, Springer, vol. 8(1), pages 73-86, January.
  2. De Angelis, Tiziano & Ferrari, Giorgio, 2014. "A stochastic partially reversible investment problem on a finite time-horizon: Free-boundary analysis," Stochastic Processes and their Applications, Elsevier, vol. 124(12), pages 4080-4119.
  3. de Angelis, Tiziano & Ferrari, Giorgio, 2014. "A Stochastic Reversible Investment Problem on a Finite-Time Horizon: Free Boundary Analysis," Center for Mathematical Economics Working Papers 477, Center for Mathematical Economics, Bielefeld University.
  4. Stéphane Villeneuve & Erik Ekstrom, 2006. "On the Value of Optimal Stopping Games," Post-Print hal-00173182, HAL.
  5. Yuri Kifer, 2000. "Game options," Finance and Stochastics, Springer, vol. 4(4), pages 443-463.
  6. Dayanik, Savas & Karatzas, Ioannis, 2003. "On the optimal stopping problem for one-dimensional diffusions," Stochastic Processes and their Applications, Elsevier, vol. 107(2), pages 173-212, October.
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