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Phase-Type Distributions and Optimal Stopping for Autoregressive Processes

Published online by Cambridge University Press:  04 February 2016

Sören Christensen
Affiliation:
Christian-Albrechts-Universität zu Kiel
Corresponding
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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.

Type
Research Article
Copyright
© Applied Probability Trust 

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