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.

The deal is Hellman & Friedman’s second buyout of an insurance-related company since August, when it agreed to purchase Hub International Inc. in a $4.4 billion transaction, the largest takeover of a U.S. insurance broker on record, according to data compiled by Bloomberg. Private-equity firms including KKR & Co. and CVC Capital Partners Ltd. have made deals in the insurance industry to take advantage of steady cash flow and low capital expenditure.

“We believe Applied Systems is a uniquely positioned company in the global insurance software market,” David Tunnell, a Hellman & Friedman managing director, said in the statement. The company’s software allows insurance agencies, brokers and customers to exchange data and information.

Hellman & Friedman, based in San Francisco, was started in 1984 and is led by Philip Hammarskjold. The firm was founded by Hellman, who died in 2011, and Tully Friedman, who runs Friedman Fleischer & Lowe LLC, a San Francisco-based firm that invests $50 million to $200 million in companies.

Hellman & Friedman is deploying its seventh fund, with more than $8.9 billion, and has invested in more than 75 companies over its history, according to its website. Its insurance transactions include reinsurer PartnerRe Ltd. and Sedgwick Claims Management Services Inc. Previous insurance deals include reinsurers Arch Capital Group Ltd. and GeoVera Insurance Group.

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