The British insurer Prudential PLC’s deal to buy American General Corp. has set off speculation about which U.S. insurer will be bought next and whether the buyer will be domestic or foreign.

European bank insurance giants such as France’s Axa and the Dutch insurer Aegon NV, as well as multiline insurers such as Germany’s Allianz, have all been building their U.S. business through acquisition for the past several years. But some analysts in Europe are saying these companies may choose to focus on growing their business on their home continent.

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