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Phase-Type Distributions and Optimal Stopping for Autoregressive Processes

Part of: Sequential methods Stochastic processes

Published online by Cambridge University Press:  04 February 2016

Sören Christensen
Sören Christensen*
Affiliation:
Christian-Albrechts-Universität zu Kiel
*
∗ Postal address: Mathematisches Seminar, Christian-Albrechts-Universität zu Kiel, Ludewig-Meyn-Str. 4, 24098 Kiel, Germany. Email address: christensen@math.uni-kiel.de
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Abstract

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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.

Keywords

Autoregressive processthreshold timephase-type innovationoptimal stopping

MSC classification

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

Information

Type
Research Article
Information
Journal of Applied Probability , Volume 49 , Issue 1 , March 2012 , pp. 22 - 39
Copyright
© Applied Probability Trust 

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