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

Alessandro Milazzo ()
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Alessandro Milazzo: University of Turin

Journal of Optimization Theory and Applications, 2024, vol. 203, issue 1, No 14, 336-358

Abstract: 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.

Keywords: Optimal stopping; Monotone stopping boundary; Time-inhomogeneous diffusions; Partial information; 60G07; 60G40; 60J60; 49N30; 35R35 (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s10957-024-02514-2

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