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

Andrea Bovo and Tiziano De Angelis

Stochastic Processes and their Applications, 2025, vol. 182, issue C

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.

Keywords: Zero-sum stochastic games; Optimal stopping; Singular control; Saddle point; Free boundary problems; Skorokhod reflection; Absorbed and controlled diffusions (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1016/j.spa.2024.104555

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