In this paper, we study the general problem of optimal portfolio selection with fixed transactions costs in the presence of jumps. We extend the analysis of Morton and Pliska to this setting by modeling the return processes of the risky assets in the investor's portfolio as jump-diffusion processes and derive the expression for the related optimal stopping time problem of a Markov process with jumps and explicitly solve it in the situation when the portfolio consists only of one risky asset. We also provide an asymptotic analysis of our model with one risky asset following the ideas of Wilmott and Atkinson. In the process, we also obtain a solution for the "Merton problem" generalized to the situation when there is credit risk. Finally, we consider the case where the drift of the stockprice process is random and unobservable and obtain expressions for the optimal trading policies.