The inverse first-passage problem and optimal stopping

2015/08/31 by Erik Ekström, Svante Janson, Ekström, Erik +1 · 1 citation
Mathematics · #FOS: Mathematics #Probability (math.PR) #math.PR

paper · pdf · doi:10.48550/arxiv.1508.07827

arxiv created 2015/08/31 · arxiv updated 2015/09/01

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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