Anything is possible if you have a lot of money, but we have never heard of "private jet boats" from Naples except for the very wealthy "Jet Setters" who are willing to spend thousands of dollars. Renting a boat in Italy is very expensive and from Naples it would even be more expensive since any destination (such as Capri, Positano, etc) is a long distance (at least 45 min by the jet boat). Many private tours will tell you that they will take you by jet boat to Capri, but in reality what they are doing is taking you on the regularly scheduled jet boats that carry several hundred other people. However, it is possible to hire a private boat for tours around the island of Capri although it does not make much financial sense unless you have a large group. There are plenty of regular boat tours around Capri that you can simply join once you arrive at Capri's port of Marina Grande.