Lloyd's of London says the US terror attacks have cost its business £1.3bn.
This is below analysts' expectations of a bill of up to £2bn.
The overall cost of the attacks is expected at least to match the record £13.8 bn paid out for Hurricane Andrew in 1992.
However, the Lloyd's insurance market has admitted that the long-term impact of the attacks has yet to be calculated.
Lloyd's underwriting syndicates are expected to be the first to be called upon for money from the losses. In addition, there is the Lloyd's central fund, valued at £323m; and the more general Lloyd's capital base, estimated at £18bn.
Less well known is that Lloyd's has been required to hold a separate reserve fund in the US since the outbreak of the Second World War. This fund is currently valued at £4bn but, as it has never been used, the rules for doing so are somewhat unclear.
The US fund is controlled by the insurance commissioners of the states in which Lloyd's is allowed to trade.
Lloyd's chairman Sax Riley says: "Arriving at an estimate for a marketplace as complex as Lloyd's was always going to take longer than for a single insurance company, especially for a situation which is still changing rapidly.
"While a figure of this size will have a significant impact on the Lloyd's market, the market's strong capital base will absorb this loss."
Mr Riley adds: "The size of our asset base, the spread of the losses and the resilience of the reinsurance programmes in place are important in coming to this conclusion."