A fourth and rather simple answer was part of the plot of an episode of Futurama. The solution that Philip J. Fry accidentally found is to simply hook up with your young hot Granny and become your own Grandfather.
A new paradox (or confusion, at least) presents itself that I did not initially consider. In the canon of Futurama, it is said that Fry's astounding stupidity and lack of common sense (along with a lack of a certain brain wave) is indeed caused by this self-Grandfathering event. It was then this very stupidity that caused him to kill his Pep Pep and fuck his (past) future Nana.
I guess it's an extreme form of inbreeding. This is what we can consider the "Past Nastification" paradox.
You can't say it won't happen.