2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/208456In this paper we consider the problem of pricing a perpetual American put option in an exponential regime-switching Lévy model. For the case of the (dense) class of phase-type jumps and finitely many regimes we derive an explicit expression for the value function. The solution of the corresponding first passage problem under a state-dependent level rests on a path transformation and a new matrix Wiener-Hopf factorization result for this class of processes.22 pages, 3 figures. Tp appear in Finance and Stochastics,Pricing of SecuritiesProbability60K15, 90A09text