In recent years we have seen the success of wireless communications in unlicensed frequency bands, mainly driven by the 802.11 standard. The clear trend in the growth of traffic demand suggests that spectrum scarcity will be a serious threat to reach the capacity needs in the near future. Looking for more available spectrum, regulators have already begun to study secondary assignments in licensed bands, based on the recent cognitive network paradigm. In this context, we focus our work in the analysis of optimum spectrum allocation mechanisms. We introduce a stochastic model to formulate the problem, considering primary users' activity and a periodically scheduled assignment scheme. To solve the problem we propose a novel robust solution, which we argue is superior to an expectation based approach, comparing both alternatives through extensive simulations.