The Annals of Applied Probability

The inverse first-passage problem and optimal stopping

Erik Ekström and 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.

Article information

Source
Ann. Appl. Probab. Volume 26, Number 5 (2016), 3154-3177.

Dates
Received: August 2015
First available in Project Euclid: 19 October 2016

Permanent link to this document
https://projecteuclid.org/euclid.aoap/1476884314

Digital Object Identifier
doi:10.1214/16-AAP1172

Mathematical Reviews number (MathSciNet)
MR3563204

Zentralblatt MATH identifier
1351.60110

Subjects
Primary: 60J65: Brownian motion [See also 58J65]
Secondary: 60G40: Stopping times; optimal stopping problems; gambling theory [See also 62L15, 91A60]

Keywords
Inverse first-passage problem optimal stopping nonlinear integral equation

Citation

Ekström, Erik; Janson, Svante. The inverse first-passage problem and optimal stopping. Ann. Appl. Probab. 26 (2016), no. 5, 3154--3177. doi:10.1214/16-AAP1172. https://projecteuclid.org/euclid.aoap/1476884314


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