I just wonder, whether the possessive can be used in the sentence bellow (my intuition says "yes" but I'd need some natve feedback):
My final point of criticism of the classical approaches to verbal irony concerns their disregarding the fact that saying the opposite of what one means is patently irrational.
Thanks a lot.
The model is 'concerns their <noun>'. Disregarding (in that context) is a gerund (verbal noun). You could equally well say 'concerns their disregard for...' (in which 'disregard' has given up all pretence of being a verb, and is itself a noun)