Exact Simulation of the Extrema of Stable Processes

06/05/2018

∙

by   Jorge Ignacio González Cázares, et al.

∙

0

∙

share

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.