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Stopping spikes, continuation bays and other features of optimal stopping with finite-time horizon

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  • Tiziano De Angelis
Abstract
We consider optimal stopping problems with finite-time horizon and state-dependent discounting. The underlying process is a one-dimensional linear diffusion and the gain function is time-homogeneous and difference of two convex functions. Under mild technical assumptions with local nature we prove fine regularity properties of the optimal stopping boundary including its continuity and strict monotonicity. The latter was never proven with probabilistic arguments. We also show that atoms in the signed measure associated with the second order spatial derivative of the gain function induce geometric properties of the continuation/stopping set that cannot be observed with smoother gain functions (we call them \emph{continuation bays} and \emph{stopping spikes}). The value function is continuously differentiable in time without any requirement on the smoothness of the gain function.

Suggested Citation

  • Tiziano De Angelis, 2020. "Stopping spikes, continuation bays and other features of optimal stopping with finite-time horizon," Papers 2009.01276, arXiv.org, revised Jan 2022.
    • Handle: RePEc:arx:papers:2009.01276
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    References listed on IDEAS

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    Cited by:

    1. Th'eo Durandard & Matteo Camboni, 2024. "Comparative Statics for Optimal Stopping Problems in Nonstationary Environments," Papers 2402.06999, arXiv.org, revised Jul 2024.

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