JUNEAU — State officials in Alaska are proposing a program to address high-cost health insurance claims in hopes of stabilizing rising rates on the individual policy market.

Just two companies — Premera Blue Cross Blue Shield and Moda Health Plan Inc. — serve the individual market in Alaska and have filed for double-digit rate increases each of the past two years. State officials say that’s not sustainable. They hope that reviving a high-risk pool to handle claims for the costliest conditions will bring some relief.

The idea is to spread the cost of those claims across all insured markets, rather than to have them just be borne by the smaller individual market.

The claims would be handled through the Alaska Comprehensive Health Insurance Association, which before the federal health care law provided insurance to Alaska residents who had been denied coverage. Under the proposal, insurers would transfer premiums for those consumers to the program, said Division of Insurance Director Lori Wing-Heier.

The hope is to ease high rate increases by taking high-risk claims from the individual market and having more than 220,000 Alaskans pay a portion of those claims rather than 22,000, she said. There would be an assessment passed on to insured Alaskans to contribute to the pool, she said. The cost of that is not yet known. But it’s not the intent to make it so expensive that people who have insurance would no longer be able to afford it, she said.

Wing-Heier told lawmakers Tuesday that without a change, the state runs the risk of the individual market going into a “death spiral,” with people potentially forced from the market by the high rates. The state struggles with high health care costs and that has translated to high insurance costs, she said.

Wing-Heier said the goal of the proposal from Gov. Bill Walker is to minimize the size of rate increases and provide some stability to the market. With the state down to two insurers in the individual market, there’s concern with how long they continue to incur the losses they have, she said.

Both Premera and Moda experienced “significant losses” in 2014 and 2015, according to the Division of Insurance. Last year, each filed for average rate increases of close to 40 percent. Early indications this year suggest continued losses and likely rate increases for next year of more than 25 percent, the division said.