The past two years of wildfires have shown that even insurers are struggling to predict the risks associated with climate change. The consequences of that failure could be profound, experts say: The very industry that’s meant to stabilize society in the face of climate change is itself being destabilized by climate change, threatening to make it harder for people to cope with the rising tempo of disasters.

The state’s homeowners insurers lost a total $20 billion in the 2017 and 2018 wildfires, according to an analysis published in October by Milliman, an actuary and consulting firm. That’s twice the industry’s cumulative profits since major wildfires in 1991. A line of business that was until recently profitable is now unprofitable, the authors wrote, “exposed to a severe peril that is neither easily measured nor fully understood.”

Eric Xu, an actuary at Milliman’s San Francisco office and one of the report’s authors, said that the shock of the California wildfires echoes Florida after Hurricane Andrew in 1992, which caused $28 billion in damage and caused the failure of a dozen insurers.

But the threat facing insurers in California is in one sense trickier: After Andrew, many national insurers stopped writing coverage in Florida. But Mr. Xu said California represents too great a share of total revenue for most national insurance companies to just walk away from the state altogether.

Unable to leave, insurers have sought other solutions to protect themselves from rising wildfire costs. But those changes highlight the obstacles facing insurers as climate change worsens.

One fix is for insurers to buy what’s called reinsurance — a sort of insurance for insurers — providing payments if claims rise beyond a certain level. But as the risks from climate change have grown, reinsurance companies have raised the cost of the protection they offer.

For insurance companies, the most obvious response is to pass the costs on to customers in the form of higher prices. California insurers filed 80 requests for rate increases in 2018, more than double the number of requests in 2015, according to data provided by the state.