The Association of Lloyd's Names (ALM) has projected pure year profits of 16.5% and 17.5% on capacity respectively for the 2002 and 2003 years of account.
It said this return would be subject to average claims and before member agents' commission.
The ALM said non-marine and marine rates were currently so high that even if they were to fall by as much as 25% over the next 12 months, they would still be at a similar level to 1995, when Lloyd's made pure year profits of 10% of capacity.
The statement follows AGM releases or trading statements from Lloyd's insurers, including Amlin, Hiscox, RJ Kiln, Wellington, Beazley, Meacock, Advent, Sackville, Faraday, SVB, Cox and Abacus, stating positive trading conditions, and predicting strong profits for 2004.
