The inverse first-passage problem and optimal stopping

Erik Ekström; Svante Janson

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arXiv · 1508.07827

The inverse first-passage problem and optimal stopping

Erik Ekström·Svante Janson

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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.

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Erik Ekström, Svante Janson. 2015-08-31. The inverse first-passage problem and optimal stopping. https://arxiv.org/abs/1508.07827

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