Journal of Applied Probability

Phase-type distributions and optimal stopping for autoregressive processes

Sören Christensen

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Abstract

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

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

Dates
First available in Project Euclid: 8 March 2012

Permanent link to this document
https://projecteuclid.org/euclid.jap/1331216832

Digital Object Identifier
doi:10.1239/jap/1331216832

Mathematical Reviews number (MathSciNet)
MR2952880

Zentralblatt MATH identifier
1254.60051

Subjects
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]

Keywords
Autoregressive process threshold time phase-type innovation optimal stopping

Citation

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. https://projecteuclid.org/euclid.jap/1331216832


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