American International Group agreed to sell mortgage insurer United Guaranty Corp. to Arch Capital Group Ltd. as Chief Executive Peter Hancock works to simplify his company and free up capital to return to shareholders.

The deal is valued at $3.4 billion including $2.2 billion in cash and the rest in Arch securities, New York-based AIG said Monday in a statement. AIG will retain a portion of mortgage-insurance business originated from 2014 through 2016 through a previously disclosed intra-company risk transfer deal.

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