Insurance companies make money in one or both of two ways: On the underwriting and investing the float. The investment returns on the float is where the real money is. Berkshire Hathaway is the poster child for this. So many insurance companies are willing to lose money on the underwriting in order to increase their market share and make it back up in the float. The reinsurance companies are playing the same game. So there is sort of an international game of chicken to see who is willing to exchange the most underwriting losses for market share. In the last few years there have been some big losses which have smacked the reinsurance companies, so they are no longer willing to take underwriting losses. That means local insurers have to jack their rates.
I'm a bit fuzzy on the details, but I recall a few years ago Warren Buffet saying BRK's share of the reinsurance market was shrinking because they weren't willing to take under writing losses. But I saw recently they were moving back into markets that other reinsurers had left.