Abstract
Given a survival distribution on the positive half-axis and a Brownian motion, a solution of the inverse first-passage problem consists of a boundary so that the first passage time over the boundary has the given distribution. We show that the solution of the inverse first-passage problem coincides with the solution of a related optimal stopping problem. Consequently, methods from optimal stopping theory may be applied in the study of the inverse first-passage problem. We illustrate this with a study of the associated integral equation for the boundary.
Citation
Erik Ekström. Svante Janson. "The inverse first-passage problem and optimal stopping." Ann. Appl. Probab. 26 (5) 3154 - 3177, October 2016. https://doi.org/10.1214/16-AAP1172
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