Very rich fathers generally havestingysons.

Stingy : mean; ungenerous; miserly.
Reckless : heedless of danger or the consequences of one's actions; rash or impetuous.
Careless : not giving sufficient attention or thought to avoiding harm or errors.
Spendthrift : a person who spends money in an extravagant, irresponsible way.
Miserly : of or characteristic of a miser.
Antonym of Stingy is Spendthrif