Outside of dictators, I would say Ashur is likely the wealthiest, with Mr House as second (assuming he won).

Ashur has a steel factory monopoly and hundreds of slaves. If the disease is cured, his slave population will be able to grow naturally, reducing overhead costs even further. His goal is to expand Pittsburgh and arm his soldiers. It's unclear if he is selling his steel or armaments, but I will count it as assets. This massive wealth is comparable to Andrew Carnegie or Alfred Krupp. Coincidentally, the Pittsburgh steel mills were originally owned by Carnegie. It was very profitable due to the large coal resources in the area as well as the extensive railway system.

Mr. House is practically running an asset management company. He takes a cut from all casino profits, 2,000 cap entrance fees from each tourist, and 50% of all F&B sold in the city. After winning the war, he controls both a robot army and an electrical grid. Electricity is a monopoly, and his army defends tourists. He's not like anyone in history, but America has electricity monopolies to this day. It's not as profitable as steel, or at least in a Fallout setting, but it's value comes from the power over others. As an old world billionaire, I'm sure he understands how to further grow his investments beyond tourism. Before the bombs, he used to build computers, military equipment, rocket ships, and robots. With his advance knowledge of industrialization, it is likely that he will become the richest person in Fallout.