We consider a simultaneous wireless transfer of information and power in a two-way relaying network, where a decode-and-forward protocol is employed for data exchange between two source devices at different rates. The data exchange is accomplished in two time phases (TPs) with possibly asymmetric TP ratios, where the relay is powered by the source devices in the first phase through simultaneous wireless information and power transfer (SWIPT) either by power splitting (PS) or by time switching (TS). For the network, resource allocation of the PS and TP ratios for the PS-based SWIPT and that of the TS and TP ratios for the TS-based SWIPT are studied to minimize the system outage probability. We first solve the joint optimization problem of each case with the instantaneous channel state information and then propose suboptimal schemes utilizing one or two values for the TP ratio to lower the implementation complexity. The results from analysis and simulation show that the proposed schemes outperform the benchmark scheme with equal resource allocation and that the gain gets more prominent as the rates of the data exchanged or the relay locations become more asymmetric.