A processes for effecting the cationic polymerization of olefins in a controlled manner that includes the step of contacting olefin monomers and a catalytically effective amount of an initiating composition containing (A) a recyclable aluminum, gallium, or indium perfluorinated organosulfonate, (B) a solubilizing agent, (C) an initiator selected from the group consisting of (i) carbocation synthons, (ii) halogenium ion synthons, (iii) Brønsted acids, and (iv) silicenium ion synthons, and optionally (D) a nucleophilic additive. The invention further includes a process for recycling aluminum, gallium, or indium perfluorinated organosulfonates that includes the steps of aqueous extraction and dehydration. A novel initiator system is also disclosed.