Lloyd's is considering appointing two banks to represent the interests of Names and managing agents.
At a private market meeting this morning, it was proposed that the financial institutions help implement recommendations by Lloyd's chairman Sax Riley's strategy group.
Last April, the group was created to discuss the way the market could move forward. Management consultancy firm Bain & Co, which assisted the group, made its recommendations this month.
It was suggested that Lloyd's should end Names with unlimited liability, the annual venture and three year accounting.
It is thought the two banks would independently examine the value of Names' underwriting rights and the potential to buy them out.
They would also look at how managing agencies may be involved in buying out unlimited liability Names' capacity.
The institutions could then work together to agree on a sum.
Lloyd's spokesman Adrian Beeby said a meeting of market members had taken place to explain the proposals in greater detail.
"We can confirm that there is a proposal to appoint banks to represent the interest of managing agencies and Names.
"This proposal will now go forward for consultation as we want to hear the market's views on how a fair valuation can be achieved," he said.
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