Phasetype distributions, autoregressive processes and overshoot

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 phasetype distributions we determine the joint distribution of this two quantities and apply this result to problems of optimal stopping. Using a principle of continuous fit this leads to explicit solutions