LOS ANGELES (Bloomberg) — 21st Century Insurance Group, a California-based car insurer, agreed to sell the rest of its shares to American International Group after AIG increased its offer 11 percent to $813 million.The world's largest insurer raised its cash bid to $22 a share for the 39 percent of 21st Century it doesn't already own, the New York-based company said in a statement today.

21st Century's board, which hadn't responded to a January 24 bid of $19.75 a share, unanimously approved the higher offer yesterday. Shares closed at $16.59 before the first overture.

Insurers are vying for a bigger slice of the $164 billion a year in auto insurance premiums as declining accident rates lead to fewer claims. The deal will give AIG a larger presence selling policies over the Internet and telephone, the model used by Geico Corporation, which is owned by Warren Buffett's Berkshire Hathaway Inc.

"By bringing in 21st Century they can do some consolidation and save costs" on call centres and marketing, said Paul Newsome, analyst at St. Louis-based A.G. Edwards & Sons, who has a "buy" rating on AIG shares. "The higher price is still not a lot of money for AIG."

A group of 21st Century's minority investors had sued to block a buyout at the first price offered by AIG. A 21st Century committee of non-AIG-linked board members endorsed the higher offer.

"They were able to convince AIG to give them a little more to put any kind of doubts to rest there wasn't a fair deal here," Newsome said.

21st Century shares gained 75 cents, or 3.6 percent, to $21.75 in New York Stock Exchange trading. They traded between $20.75 and $21.80 from the day after the first bid until yesterday's close, as investors anticipated a higher offer. AIG shares fell 40 cents, or .6 percent, to $72.07.

Bruce Marlow, chief executive officer of 21st Century, will lead a combined entity that includes AIG's own direct auto insurer. Policy sales for the two operations were $2.9 billion last year. AIG hasn't yet decided the name of the new unit, said spokesman Chris Winans. The deal is expected to be completed in the third quarter, AIG said.

"AIG can capture the benefit that can come from integrated personalised operations, our technology platform and the creation of a direct-to-consumer company similar in scale to Progressive Direct," Marlow said in a February 27 conference call after the company announced its earnings.

Marlow was chief operating officer at Mayfield Village, Ohio-based Progressive Corporation, the third-largest US auto insurer, from 1988 until 1996.

"Management at 21st Century is very good," said Cliff Gallant, an analyst with Keefe, Bruyette & Woods in New York who has an "outperform" rating on AIG. "Elevating Marlow to being in charge of AIG's direct distribution nationally makes a lot of sense."

The deal may add $640 million to AIG's pretax earnings by 2010 on increased sales and cost savings, wrote Charles Gates, analyst at Credit Suisse Group in New York, in a May 10 research note.

AIG will double its market share to six percent by 2010, becoming the number five US car insurer, up from number nine in 2005, said Gates, who ranks AIG shares "outperform." Geico, based in Chevy Chase, Maryland, will likely move to number three from four, he said. Bloomington, Illinois-based State Farm Mutual Automobile Insurance Company is the number one auto insurer, followed by Allstate Corporation of Northbrook, Illinois.

Woodland Hills, California-based 21st Century insures more than 1.5 million cars and operates in 18 US states, according to the statement. It has added operations in New Jersey, Colorado, Minnesota, Missouri, Wisconsin and New York in the past year. AIG has had a stake in 21st Century since 1994.

Darren Robbins, a lawyer in San Diego representing minority 21st Century investors in their lawsuit, didn't return calls.

Bank of America and JPMorgan Chase & Co are advising AIG. Lehman Brothers Holdings is advising the committee of 21st Century that reviewed the offer, AIG said.