You are talking about fraud (I'm assuming wire fraud, chargebacks, stolen accounts, etc.) which I would put in a different category of risk for a financial institution than money laundering. These activities would lead to direct losses, whereas money laundering would not.
I assume allowing laundered money through your institution is of less concern, since it would not lead to a direct loss to the institution. This is assuming you are not knowingly allowing the laundering to occur and you are following all AML and KYC regulations meant to prevent money laundering. If these standards are not met, it may lead to fines and having regulators watch your institution more closely.
Wire fraud and stolen account schemes generally get eliminated/caught because of laundering issues, not because of how they do the actual fraud; and for large cases of fraud / large stolen accounts, the laundering capacity limits the total amount.
Good AML provisions help reduce your fraud losses, even if you decide to make some "exceptions" for your VIP customers.
It's actually the opposite of fraud, because laundering money involves transactions which frequently make a great deal of money for the bank. Look at the fat fees Goldman Sachs earned setting up the 1MDB transactions for Malaysia. There was a lot of speculation around the financial crisis that banks opened their doors to money launderers because it was the only available liquid asset available in sufficient quantity to keep them solvent. So the bank actually has an incentive to launder money, so long as it can do so without being caught and fined or having its employees go to jail.
The point below is true though. Many of the same markers of fraud indicate money laundering, and having a good risk program can reduce both if that's your intention.
I assume allowing laundered money through your institution is of less concern, since it would not lead to a direct loss to the institution. This is assuming you are not knowingly allowing the laundering to occur and you are following all AML and KYC regulations meant to prevent money laundering. If these standards are not met, it may lead to fines and having regulators watch your institution more closely.