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On the saddle point of a zero-sum stopper vs. singular-controller game

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  • Bovo, Andrea
  • De Angelis, Tiziano

Abstract

We construct a saddle point in a class of zero-sum games between a stopper and a singular-controller. The underlying dynamics is a one-dimensional, time-homogeneous, singularly controlled diffusion taking values either on R or on [0,∞). The games are set on a finite-time horizon, thus leading to analytical problems in the form of parabolic variational inequalities with gradient and obstacle constraints.

Suggested Citation

  • Bovo, Andrea & De Angelis, Tiziano, 2025. "On the saddle point of a zero-sum stopper vs. singular-controller game," Stochastic Processes and their Applications, Elsevier, vol. 182(C).
    • Handle: RePEc:eee:spapps:v:182:y:2025:i:c:s0304414924002631
    DOI: 10.1016/j.spa.2024.104555
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    References listed on IDEAS

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    1. Damien Lamberton & Mohammed Mikou, 2008. "The critical price for the American put in an exponential Lévy model," Finance and Stochastics, Springer, vol. 12(4), pages 561-581, October.
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    4. Andrea Bovo & Tiziano De Angelis & Jan Palczewski, 2023. "Zero-sum stopper vs. singular-controller games with constrained control directions," Papers 2306.05113, arXiv.org, revised Feb 2024.
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    9. Tiziano De Angelis & Erik Ekstrom, 2016. "The dividend problem with a finite horizon," Papers 1609.01655, arXiv.org, revised Nov 2017.
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