Most of Insurance Australia Group's near 4 percent growth in premiums in the year ended June in New Zealand came from price increases, rather than new sales.
What's more, the price of insurance premiums is likely to continue rising faster than the rate of inflation, 1.6 percent in the year to the end of June.
IAG is the largest general insurance company in New Zealand with about 45 percent of the market and operating through the NZI, State, AMI brands and now, from the beginning of July, the Lumley brand.
IAG's New Zealand chief executive, Jacki Johnson, said her company needs to make sure that insurance stays affordable, but that investors are also rewarded.
"One of the things that we're very mindful of in New Zealand is when we're ranked number three in the world for natural perils of large natures.
"To keep insurance available, we really need to make sure that we balance all stakeholders, so making sure insurance stays accessible and affordable, making sure see it's the right place to invest and then looking at making sure we can secure reinsurance and our licensing under the Reserve Bank.
"For us to have a strong performance in the years that we price appropriately means that we can make sure we keep insurance available and also as affordable as we can for the risks that we take in New Zealand."
Ms Johnson said insurance premiums are likely to rise further.