This paper investigates power splitting for full-duplex relay networks with wireless information and energy transfer. By applying power splitting as a relay transceiver architecture, the full duplex information relaying can be powered by energy harvested from the source-emitted radio frequency signal. In order to minimize outage probability, power splitting ratios have been dynamically optimized according to full channel state information (CSI) and partial CSI, respectively. Under strong loop interference, the proposed full CSI-based and partial CSI-based power splitting schemes achieve the better outage performance than the fixed power splitting scheme, whereas the partial CSI-based power splitting scheme can ensure competitive outage performance without requiring CSI of the second-hop link. It is also observed that the worst outage performance is achieved when the relay is located midway between the source and destination, whereas the outage performance of partial CSI-based power splitting scheme approaches that of full CSI-based scheme when the relay is placed close to the destination.