Hellman & Friedman LLC, the private- equity firm co-founded by Warren Hellman, agreed to acquire insurance software company Applied Systems Inc. in a buyout valued at $1.8 billion.

Hellman & Friedman is joining with private-equity firm JMI Equity in acquiring University Park, Illinois-based Applied Systems from Bain Capital LLC, the firms said in a statement today. Members of Applied Systems management will hold a significant ownership stake in the company following the acquisition, according to the statement.

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