They survived Charley and Frances, but Ivan could be a hurricane too far for reinsurers.
Munich Re chairman Nikolaus von Bomhard warned that the impact of the category 5 storm on densely-populated areas of Florida would affect its full year profit target of bn.
Munich Re director Georg Daschner said losses from the hurricane season so far were "heavy, but we do not consider them to be catastrophic".
Ivan is predicted to miss Florida and hit the US mainland in the area of Louisiana and Alabama, where there are low levels of insurance and low insured property values.
But hurricanes don't always do what they are expected to.
Catastrophe modelling firm Eqecat warned that if Ivan made landfall near Florida's Tampa Bay/St Petersburg area, insured losses could exceed $35m.
Category 5 hurricanes have wind speeds in excess of 150mph. The last category 5 storm to hit the mainland US was Hurricane Andrew in 992, causing $25bn (adjusted for 2004) in damage and killing 43 people.
Hurricane Ivan has killed more than 60 people in the Caribbean. The storm clipped the western tip of Cuba on Monday evening.
It said the net financial impact of Charley was £306m, representing 2% of the market's capacity.
Lloyd's said that losses from Charley were "not likely to have a significant impact on the financial market or on profit projections".
It said that and that it was well within normal business planning assumptions. Estimates are not yet available for Hurricane Frances.