The inverse first-passage problem and optimal stopping
Probability
2015-09-01 v1
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.
Cite
@article{arxiv.1508.07827,
title = {The inverse first-passage problem and optimal stopping},
author = {Erik Ekström and Svante Janson},
journal= {arXiv preprint arXiv:1508.07827},
year = {2015}
}