An arbitrator has no power to fix the scope of the arbitrator’s jurisdiction. Jurisdiction must be fixed by the terms of reference of the arbitration. Its scope must be objectively ascertainable in advance of the arbitration.
An arbitrator cannot make a decision conferring jurisdiction on the arbitrator that is not possessed in law. That is why an arbitrator cannot without specific powers determine whether a contract has been validly terminated because this would result in there being no dispute to arbitrate.