Lord Levene calls on Lloyd's to attack "markets of the future", according to reports.
Lloyd's is set to expand in to emerging markets in Asia and Latin America and oil rich countries in the Gulf, according to reports this morning.
The Associated Press said Lloyd's has warned that a shift in world power can not be ignored.
Lloyd's chairman Lord Levene is also reported to have hit back at pricing criticism directed at the insurance market following threats from major Atlantic hurricanes including Gustav.
Up to 40% of Lloyd's premium income comes from the US. However, Levene insists the group must build on "markets of the future" in order to leave a strong business for successors.
In his annual speech to business leaders in London, Levene said: "The balance of power in the world has truly shifted, and we have to rapidly wake up to that,"
Levene also said that Lloyd's is already building its business in China and elsewhere in Asia, but has got no further in India "despite promises from the Indian Government to remove the protectionism which has lasted for far too long."
"We look forward to the day when we can play our part too in the development of the hugely successful Indian economy," he added.
According to the report, Levene said that the company was still deciding how to develop its business in the Gulf. He also said that Lloyd's must run its business in the US in a way that allows it to pay out in the wake of hurricanes like Gustav, Hanna, Ike and Josephine.
He said: "I am still amazed at the industry's collective madness in not maintaining prices at economic level."
Finally, Levene also called on the British government to speed up a potential change to the way Lloyd's is taxed in Britain.