We study the perpetual American option characteristics in the case where the underlying dynamics involve a Brownian motion and a point process with a stochastic intensity. No assumption on the distribution of the jump size is made and we work with an arbitrary positive or negative jump. After...

In this article the problem of the American option valuation in a L´vy process setting is analyzed. The perpetual case is first considered. Without possible discontinuities (i.e. with negative jumps inthe call case), known results concerning the currency option value as well as the exercise...