%0 Journal Article
%T The inverse first-passage problem and optimal stopping
%A Erik Ekstr£żm
%A Svante Janson
%J Mathematics
%D 2015
%I arXiv
%X 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.
%U http://arxiv.org/abs/1508.07827v1