W.R. Berkely Corp. said Friday that Japanese insurer Mitsui Sumitomo Insurance Co. Ltd. has agreed to buy 15% of the Greenwich, Connecticut-based insurer through an agreement with the Berkley family.

The specialty insurer, founded by Executive Chairman William R. Berkley in 1967, is the second-largest surplus lines insurer in the United States, according to Business Insurance’s most recent ranking. Last year, the company reported $14.21 billion in gross written premium.

Under the terms of the deal, Mitsui Sumitomo has entered into an agreement with a company owned by members of the Berkley family and related trusts to buy shares through the open market or private transactions.

Mr. Berkley owns about 21% of the insurer, according to filings with the U.S. Securities and Exchange Commission, but neither the family nor the company will be selling shares under the arrangement, a W.R. Berkley statement said.

Once Tokyo-based Mitsui Sumitomo has acquired 12.5% of the W.R. Berkley shares, the Berkely family will recommend the election of a representative of the Japanese insurer to the board, the statement said.

The Berkley family will continue to have two seats on the board. In addition to Mr. Berkely, his son, President and CEO W. Robert Berkely Jr. is a board member.

“The agreements between MSI and the Berkley family will not have any effect on the day-to-day operations of the company, nor will these arrangements reduce the Berkley family’s commitment to the company,” the statement said.

W.R. Berkley and Mitsui Sumitomo have collaborated on reinsurance in the past, Robert Berkley said in the statement.

“We are excited to have regular conversations with them about opportunities to leverage their international presence,” he said.

W.R. Berkley shares were up about 7% in late trading on Friday amid a sharply falling market.