This paper investigates the use of full duplex relaying (FDR) in cognitive radio systems. Cognitive FDR systems offer the advantage not only of increasing spectral efficiency by spectrum sharing but also of extending the coverage through the use of relays. Concurrent transmissions at the source and relay in FDR systems can overcome a loss of resource efficiency in a way that conventional half duplex relay (HDR) systems cannot. However, in cognitive FDR systems, the primary user experiences interference from the secondary source and relay simultaneously due to the full duplexing. Satisfying the interference constraint by simply reducing transmission power results in performance degradation for the secondary user. What is therefore needed is a way to optimize the transmission powers at the secondary source and relay. Therefore, we propose an optimal power allocation scheme based on minimizing the outage probability in cognitive FDR systems. We then analyze the outage probability of the secondary user in the noise-limited and interference-limited environments. Simulation results show that the proposed schemes achieve performance improvement in terms of outage probability.