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On the Monotonicity of the Stopping Boundary for Time-Inhomogeneous Optimal Stopping Problems

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  • Alessandro Milazzo

    (University of Turin)

Abstract

We consider a class of time-inhomogeneous optimal stopping problems and we provide sufficient conditions on the data of the problem that guarantee monotonicity of the optimal stopping boundary. In our setting, time-inhomogeneity stems not only from the reward function but, in particular, from the time dependence of the drift coefficient of the one-dimensional stochastic differential equation (SDE) which drives the stopping problem. In order to obtain our results, we mostly employ probabilistic arguments: we use a comparison principle between solutions of the SDE computed at different starting times, and martingale methods of optimal stopping theory. We also show a variant of the main theorem, which weakens one of the assumptions and additionally relies on the renowned connection between optimal stopping and free-boundary problems.

Suggested Citation

  • Alessandro Milazzo, 2024. "On the Monotonicity of the Stopping Boundary for Time-Inhomogeneous Optimal Stopping Problems," Journal of Optimization Theory and Applications, Springer, vol. 203(1), pages 336-358, October.
    • Handle: RePEc:spr:joptap:v:203:y:2024:i:1:d:10.1007_s10957-024-02514-2
    DOI: 10.1007/s10957-024-02514-2
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    References listed on IDEAS

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