So I guess I have one solution, I dont know if it is the nicest solution but it works:
On each task I add a listener that is called when the task is created. That listeners adds the initiator of the process as a owner to the task. Then you will need a filter that looks if the owner is the current user ("${currentUser()}").
The problem is, that there is appearing a small bug that I mentioned here: BUG - Filter: Key Owner is not working with value ${currentUser()}