A1 Refereed original research article in a scientific journal
Optimal stopping with variable attention
Authors: Lempa, Jukka; Saarinen, Harto; Sillanpää, Wiljami
Publisher: CAMBRIDGE UNIV PRESS
Publication year: 2025
Journal:: Advances in Applied Probability
ISSN: 0001-8678
eISSN: 1475-6064
DOI: https://doi.org/10.1017/apr.2025.10022
Web address : https://doi.org/10.1017/apr.2025.10022
Self-archived copy’s web address: https://research.utu.fi/converis/portal/detail/Publication/500333380
We consider an optimal stopping problem of a linear diffusion under Poisson constraint where the agent can adjust the arrival rate of new stopping opportunities. We assume that the agent may switch the rate of the Poisson process between two values. Maintaining the lower rate incurs no cost, whereas the higher rate requires effort that is captured by a cost function c. We study a broad class of payoff functions, cost functions and diffusion dynamics, for which we explicitly characterize the solution to the constrained stopping problem. We also characterize the case where switching to the higher rate is always suboptimal. The results are illustrated with two examples.
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Funding information in the publication:
The Foundation for Economic Education (Liikesivistysrahasto) and OP Research Foundation (grant number 20240114) are acknowledged for funding. Emmy.network is acknowledged for continued support.
