2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/212410This paper studies an optimal stopping problem for Lévy processes. We give a justification of the form of the Snell envelope using standard results of optimal stopping. We also justify the convexity of the value function, and without a priori restriction to a particular class of stopping times, we deduce that the smallest optimal stopping time is necessarily a hitting time. We propose a method which allows to obtain the optimal threshold. Moreover this method allows to avoid long calculations of the integro-differential operatorused in the usual proofs.32 pagesProbabilitytext