This letter focuses on weighted sum rate maximization with filter bank multi-carrier (FBMC) and orthogonal frequency division multiplex (OFDM) multi-carrier modulations for asynchronous device-to-device (D2D) communications. The main difficulty in power allocation with asynchronous multi-carrier transmissions is that inter-channel interference (ICI) depends on subcarriers, whereas power values should be optimized with resource block (RB) granularity. In this letter, we show that the weighted sum rate maximization problem can be solved at RB level, while still considering ICI, and that the power allocation algorithm solving this problem is distributed and leads to its global optimum. Moreover, FBMC achieves higher data rates than OFDM, thanks to its lower ICI spread.