Intertemporal continuous time portfolio selection models are rather easy to implement -they only need means and variances/covariances as input (and no higher moments). Moreover, they are able to gain closed form portfolio strategies and, as a by-product, compact pricing equations e.g. the continuous time CAPM. - However, both the tracta- bility and the theoretical content of continuous time models are closely connected with the stock price process assumed. Therefore, we introduce stock price jumps to get a more realistic representation of stock price movements. But optimization under jump risks calls for an completely new portfolio strategy. It does not work as simple as adjusting mean and standard deviation of the price process to jumps and use the old portfolio rules of the diffusion case. Instead, we have to explicitly integrate jump risks into portfolio planning via hedge terms. These hedge terms also enter pricing equations and hence, make both forms of jumps - firm-specific and market jumps - to contain systematic risk. Thus, we refute an opinion especially widespread in option pricing literature, e.g. Merton (1976), about the unsystematic character of firm-specific jump risks.