LONDON — U.K. insurer Prudential PLC Monday said it would pay $35.5 billion to buy American International Group Inc.'s Asian life-insurance business, in a deal that would make Prudential an Asian insurance giant and will allow AIG to pay back a chunk of its massive debt to the U.S. government.

The deal, which requires Prudential to launch one of the biggest rights issues in the U.K., caused Prudential's stock to fall as investors worried over a possible dilution of their shares in the company and questioned whether Prudential is overpaying for AIA.

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