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.
Citation
Sören Christensen. "Phase-type distributions and optimal stopping for autoregressive processes." J. Appl. Probab. 49 (1) 22 - 39, March 2012. https://doi.org/10.1239/jap/1331216832
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