SAN FRANCISCO — The PMI Group Inc. has announced that it will buy CGU Lenders Mortgage Insurance Ltd., Australia’s fourth-largest mortgage insurance company, from British insurer CGNU PLC for about $40 million.

The deal is expected to close in the third quarter, and it would merge CGU into PMI’s Australian subsidiary, PMI Mortgage Insurance Ltd.

CGU had $12.3 billion of insurance in force at Dec. 31, including $2.9 billion of insurance written last year. The company has about 7% of the mortgage insurance market in Australia and is the largest insurer in New Zealand.

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