Equitas and Names have refuted suggestions that proposed US asbestos legislation could lead to the insolvency of the Lloyd's reinsurance vehicle.
The draft bill proposes to set up a $140bn compensation fund for asbestos victims, designed to settle all claims.
The insurance industry is expected to contribute about $46bn.
An Equitas spokesman said: "We expect our remaining share of US liabilities to be under 5% of the $46bn. We are quite confident that our reserves are adequate and appropriate, and if we get fair assessment we would be able to pay in full."
He added: "The Bill is a very similar proposal to the one worked on last year and that failed to get through. So it is far from certain that this one will get through."
A spokesman from the Association of Lloyd's Members said: "The Asbestos Resolution Bill does provide an opportunity to solve the huge problem of asbestos litigation in the US, but it is a Bill about which there are many conflicting views.
"We believe that the reserves of Equitas are sufficient."
