Usually, “legacy” implies something positive left behind.

But that’s not the case for holders of Anthem Blue Cross and Blue Shield’s “legacy” individual health insurance policies, those that predate the Affordable Care Act. For them, the legacy tag means a big rate hike.

The Maine Bureau of Insurance approved an average premium increase of 13.4 percent for the insurer’s legacy block of 7,110 policies, which cover about 11,350 people in the state. Eric A. Cioppa, the superintendent of insurance, approved the increase after rejecting as excessive Anthem’s request for an average hike of 18.32 percent on its “legacy individual products.”

The policies are those left behind after the adoption of the ACA, said Mitchell Stein, an independent health policy consultant in Maine.

Stein said the law allows some individual policies written before the law went into force – and even a few that were written afterward – to continue for people who want to keep them, even if they don’t meet legal requirements for covering essential health conditions and out-of-pocket maximums.

Most individuals, he said, find a better deal on the ACA website, healthcare.gov, especially with subsidies that can help people with the cost. He said in some cases, families with a lot of children can get some subsidies even if their income is as high as $90,000.

But there are still some people who aren’t helped by the law and the selection of policies.

Jay Cox, who runs The Old Farm Christmas Place in Cape Elizabeth and runs a fishing boat in Alaska four months of the year, said he wasn’t able to find a better plan on healthcare.gov even though his premium on his Anthem individual policy will rise $800 this year, to $8,136, with a $2,500 deductible.

He has helped family members sign up for insurance on healthcare.gov and believes many got good deals. But when he searched for himself, the cost, co-pays and deductibles were higher than his Anthem plan.

He’s had his Anthem policy since 2009 and the average yearly increases were 4 percent, until this year. Cox was shocked when he heard about the proposed increase of more than 18 percent earlier this fall and wrote to the Bureau of Insurance to register his objection.

The actual increase, he said, was “a bit more reasonable,” but it’s still a big jump.

“I like what I’ve got, but I’m concerned if it’s going to continue,” Cox said. “I’m just going to take it year-to-year at this point.”

Stein said that’s a good approach, because premiums are likely to continue to rise. As the risk continues to be spread among a shrinking pool of people, he said insurers will have to charge enough to prepare for high costs in case a lot of the policy holders draw heavily on their coverage.

The state can even order a company to drop the policies, Stein said, although Maine has opted to keep them in place, at least for 2015.

He predicted that more people who have the policies will drop them increasingly in future years.

“Even though by inertia, people want to keep what they have, it’s worth shopping around,” Stein said.