So the psychology is that someone with a lot of money wants to pay to take an artwork and put it in a vault, never displaying it. So the reward is to know something other people don't (ie the art's location) and to exert power over people by denying them the ability to see that art. That paints what seems to be a fairly accurate psychological profile of the ultra-wealthy as a whole.
The other side of art theft is looting, usually in war and particularly by the Nazis in WW2. The interesting part of this one is how the art and auction world enabled and profited off this trade where they willingly participated in the resale of stolen artwork even though there's clear provenance back to the original owners that no one involved in auctions seemed inclined to ever research and find out. Never ask a question you don't want the answer to. Greed is such a powerful motivator.