Economics in the Harry Potter world is weird, not least because there's a single bank controlling all the money.
But who has (or needs) the biggest chamber at Gringotts? Who is the richest wizard?
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Bellatrix Lestrange was the wealthiest
Bellatrix's lifestyle makes it evident that she's very rich. She, unlike Lucius, has no children so her money has stayed her own.
Now we take a look at the Deathly Hallows book.
Chapter 26, page 437
"Make him press his hand to the door!" Griphook urged Harry,who turned his wand again upon Bogrod.
The old goblin obeyed, pressing his palm to the wood, and the door of the vault melted away to reveal a cave-like opening crammed from floor to ceiling with golden coins and goblets, silver armour, skins of strange creatures, some with long spines, others with drooping wings, potions in jewelled, and a skull still wearing it's crown.
This clearly says that Bellatrix was the richest in the wizarding world. But as she died in the battle of Hogwarts, her riches might have been given to Narcissa.
If she had given her money to Narcissa Malfoy, then the Malfoys would have been the wealthiest as they were already very wealthy. Therefore, Draco Malfoy (to whom the riches might have been inherited) may be the richest wizard in this case.
If not, it's Bellatrix.