Mr. Brindle did note, however, that companies writing reinsurance only are struggling to write now, because of the market's efficiency. Once you move a little bit down from the technical price in the reinsurance market, "suddenly everything is underwater. Everything is underpriced."

Going through the classes of business that Lancashire writes individually, Mr. Brindle said that undersupply in the retrocessional market is keeping rate reductions low.

In the property-excess area, he said Lancashire is achieving a renewal-price index in the mid-to-high 80s (or 10-to-15 percent lower than expiring prices), attributing the result to decisions to reposition layers to those that are advantageous in terms of premium-to-probable maximum loss impact.

For both property and energy, "the inefficiency of the market plays into our hands. We're able to mitigate to a large extent the overall reductions of the market by picking the deals that work and rejecting the deals that don't," he said.

Mr. Brindle also said that marine rates are "pretty much flat-lining now," noting that the market as a whole had its worst-ever year for marine business.

"What's scary is there wasn't one particularly huge event. It was just lots of frequency," he said, noting that in spite of the events, Lancashire was able to achieve a loss ratio of 50.

A final class that Lancashire writes is an aviation class known as AV52.

"We're not covering general aviation. It's only a Sept. 11 scenario that we're insuring," he said, explaining that the coverage pays out only in the event that an aircraft is hijacked and successfully flown into third-party assets.

The renewal price index for the AV52 is 88 percent, and Lancashire continues to like this class, Mr. Brindle said.

"I know it's a very macabre subject...but I think public opinion at the time showed that should this happen again, public opinion would overwhelmingly favor shooting the aircraft down--because it's better that hundreds dies than thousands do."

"So we think the event set is extraordinarily remote and it pays really good money," he said.