From the standpoint of finance and influence, the wealthiest entity in the Known World would appear to be The Iron Bank of Braavos. Every major house & government of the world has had financial dealings with the bank, and its authority in financial matters is respected by everyone across the board, regardless of political affiliation.
Much like the Lannister family of Westeros, well-known for paying their debts, the Iron Bank has a motto known throughout the Seven Kingdoms: "The Iron Bank will have its due." Its influence and power is summarized in this single statement by Tywin Lannister (GoT, S3E3):
One stone crumbles and another takes its place and the temple holds
its form for a thousand years or more. And that's what the Iron Bank
is, a temple. We all live in its shadow and almost none of us know it.
You can't run from them, you can't cheat them, you can't sway them
with excuses. If you owe them money and you don't want to crumble
yourself, you pay it back.
If restricting ourselves to the continent of Westeros alone, then the wealthiest entity would no doubt be the Lannister family themselves, with House Lannister often being touted as the richest of the great houses.