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A Dynkin game on assets with incomplete information on the return

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  • De Angelis, Tiziano
  • Gensbittel, Fabien
  • Villeneuve, Stéphane

Abstract

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.

Suggested Citation

  • De Angelis, Tiziano & Gensbittel, Fabien & Villeneuve, Stéphane, 2017. "A Dynkin game on assets with incomplete information on the return," TSE Working Papers 17-815, Toulouse School of Economics (TSE).
    • Handle: RePEc:tse:wpaper:31754
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    References listed on IDEAS

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    1. 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.
    2. Erik Ekstrom & Stephane Villeneuve, 2006. "On the value of optimal stopping games," Papers math/0610324, arXiv.org.
    3. Yuri Kifer, 2000. "Game options," Finance and Stochastics, Springer, vol. 4(4), pages 443-463.
    4. 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.
    5. Andreas Kyprianou, 2004. "Some calculations for Israeli options," Finance and Stochastics, Springer, vol. 8(1), pages 73-86, January.
    6. 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.
    7. Stéphane Villeneuve & Erik Ekstrom, 2006. "On the Value of Optimal Stopping Games," Post-Print hal-00173182, HAL.
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    Citations

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    Cited by:

    1. Tiziano De Angelis, 2018. "Optimal dividends with partial information and stopping of a degenerate reflecting diffusion," Papers 1805.12035, arXiv.org, revised Mar 2019.
    2. Tiziano Angelis, 2020. "Optimal dividends with partial information and stopping of a degenerate reflecting diffusion," Finance and Stochastics, Springer, vol. 24(1), pages 71-123, January.
    3. Fabien Gensbittel & Christine Grün, 2019. "Zero-Sum Stopping Games with Asymmetric Information," Mathematics of Operations Research, INFORMS, vol. 44(1), pages 277-302, February.
    4. Giorgia Callegaro & Claudia Ceci & Giorgio Ferrari, 2019. "Optimal Reduction of Public Debt under Partial Observation of the Economic Growth," Papers 1901.08356, arXiv.org, revised Jan 2019.
    5. Tiziano De Angelis & Erik Ekstrom & Kristoffer Glover, 2018. "Dynkin games with incomplete and asymmetric information," Papers 1810.07674, arXiv.org, revised Jul 2020.
    6. Tiziano De Angelis & Nikita Merkulov & Jan Palczewski, 2020. "On the value of non-Markovian Dynkin games with partial and asymmetric information," Papers 2007.10643, arXiv.org, revised Feb 2021.
    7. Giorgia Callegaro & Claudia Ceci & Giorgio Ferrari, 2020. "Optimal reduction of public debt under partial observation of the economic growth," Finance and Stochastics, Springer, vol. 24(4), pages 1083-1132, October.

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