Nanometer-scale resistive switching devices operated in the metallic conductance regime offer ultimately scalable and widely reconfigurable hardware elements for novel in-memory and neuromorphic computing architectures. Moreover, they exhibit high operation speed at low power arising from the ease of the electric-field-driven redistribution of only a small amount of highly mobile ionic species upon resistive switching. We investigate the memristive behavior of a so-far less explored representative of this class, the Ag/AgI material system in a point contact arrangement established by the conducting PtIr tip of a scanning probe microscope. We demonstrate stable resistive switching duty cycles and investigate the dynamical aspects of non-volatile operation in detail. The high-speed switching capabilities are explored by a custom-designed microwave setup that enables time-resolved studies of subsequent set and reset transitions upon biasing the Ag/AgI/PtIr nanojunctions with sub-nanosecond voltage pulses. Our results demonstrate the potential of Ag-based filamentary memristive nanodevices to serve as the hardware elements in high-speed neuromorphic circuits.