An incomplete market driven by a pair of Wiener and Poisson processes is considered. The range of European and American claim prices is determined.

In this paper we consider the valuation of an option with time to expiration $T$ and pay-off function $g$ which is a convex function (as is a European call option), and constant interest rate $r$, in the case where the underlying model for stock prices $(S_t)$ is a purely discontinuous process...