Irving Picard, the trustee for the liquidation of Bernard L. Madoff Investment Securities L.L.C., says he has reached a settlement with about a dozen funds and affiliates of Tremont Group Holdings Inc.

Tremont, Rye, N.Y., manages the Rye Select and Tremont families of funds, which invested money with Bernie Madoff’s firm.

An affiliate of the OppenheimerFunds acquired Tremont in 2001. Oppenheimer Funds, in turn, is a unit of Massachusetts Mutual Life Insurance Company, Springfield, Mass.

In addition to the Tremont funds, the settlement Picard negotiated includes MassMutual, MassMutual Holding L.L.C., and MassMutual’s Oppenheimer Acquisition Corp., Picard says.

The defendants have agreed to provide $1 billion in cash for a customer fund, and the cash eventually will be paid to Madoff firm customers with allowed claims, Picard says.

The proposed settlement is subject to approval by the U.S. Bankruptcy Court for the Southern District of New York.

Picard says that he already has recovered $2.6 billion for the customer fund, and that a settlement for another $5 billion recovery is under appeal.

Picard estimates he has recovered or is closing to recovering a total of $8.6 billion in assets, or about 50% of the $17.3 billion in principal lost in the Ponzi scheme by customers who filed claims.

The proposed settlement means that Madoff firm customers may be able to collect on about $3 billion in customer claims, giving those customers the potential to recover a substantial portion of their losses, according to Tremont.

The Madoff firm collapsed in 2008. Madoff told authorities he had run a Ponzi scheme that had cost investors about $50 billion. Picard is now winding down the operations of the firm through a Securities Investor Protection Act of 1970 (SIPA) liquidation process.

Lawyers at Baker & Hostetler L.L.P., New York, the court-appointed counsel for the trustee, have argued that the Rye Select and Tremont funds failed to follow up on indications that the Madoff firm could be a fraud.

Picard believes he would have won if he had taken the case to trial, but “he also recognizes the benefits of avoiding protracted litigation,” Marc Powers, a partner at Baker & Hostetler, says in a statement about the settlement.

Tremont and the other defendants in the case have vigorously denied the claims alleged by Picard, and approval of the proposed settlement should resolve the claims, Tremont says.

“Tremont is pleased to have negotiated an agreement with the trustee that gives investors in our funds the potential to recover a substantial portion of their losses incurred as a result of Madoff’s fraud,” Tremont spokesman Montieth Illingworth says in a statement. “We concluded that bringing this matter to a close, with proofs of claim preserved, was the best outcome for investors in our funds.”

“MassMutual is pleased to put this matter behind us in a manner that does not have any meaningful financial impact on the company,” MassMutual says in a separate statement.

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