I think they do as they are funding the weapons of war, including Atomic bombs and their delivery systems.
The rich want a stable economy, and a nuclear war would produce a very unstable economy. They make a lot more money from conventional wars that are limited to 3rd world nations.
If the rich wanted a stable economy, they would not destabilize it by allowing the graph that shows instability in our socio economic demographic pyramid to continue in the shape of a hockey stick that we now have.
That is nothing compared to the economic instability that would be caused by nuclear bombs going off in our major cities.