Journal of Applied Probability

Phase-type distributions and optimal stopping for autoregressive processes

Sören Christensen

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Autoregressive processes are intensively studied in statistics and other fields of applied stochastics. For many applications, the overshoot and the threshold time are of special interest. When the upward innovations are in the class of phase-type distributions, we determine the joint distribution of these two quantities and apply this result to problems of optimal stopping. Using a principle of continuous fit, this leads to explicit solutions.

Article information

J. Appl. Probab., Volume 49, Number 1 (2012), 22-39.

First available in Project Euclid: 8 March 2012

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60G99: None of the above, but in this section
Secondary: 60G40: Stopping times; optimal stopping problems; gambling theory [See also 62L15, 91A60] 62L15: Optimal stopping [See also 60G40, 91A60]

Autoregressive process threshold time phase-type innovation optimal stopping


Christensen, Sören. Phase-type distributions and optimal stopping for autoregressive processes. J. Appl. Probab. 49 (2012), no. 1, 22--39. doi:10.1239/jap/1331216832.

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