Title: Exact Simulation of the Extrema of Stable Processes,
Abstract: We exhibit an exact simulation algorithm for the supremum of a stable process
over a finite time interval using dominated coupling from the past (DCFTP). We
establish a novel perpetuity equation for the supremum (via the representation
of the concave majorants of Lévy processes) and apply it to construct a
Markov chain in the DCFTP algorithm. We prove that the number of steps taken
backwards in time before the coalescence is detected is finite.