Now that American International Group has finally closed its $5.6 billion acquisition of Validus Holdings, an unspoken question has been: What’s the next acquisition target?

The issue came up during AIG’s 2018 second-quarter earnings call, when an analyst asked that very question. AIG CEO Brian Duperreault appeared to be a bit impatient that the subject came up again but went on to explain the insurer’s ongoing acquisition strategy anyway. Choosy would be a key word.

“I have said this quite a few times in these calls. I always look for acquisitions, but we have our standards, and Validus was a great example of our standards,” Duperreault said. “It filled parts of our portfolio we didn’t have, and it added great people and capabilities to our company. We continue to look for businesses that do that.”

Duperreault acknowledged that life insurance might be one potential area for acquisition, potentially dovetailing with the insurer’s retirement planning business.

“The demographics are pretty consistent,” he said. “People are getting older. We have an international footprint. I would love to maximize that better than in the past.”

On the other hand, U.S. general insurance may also be of interest, Duperreault said. He noted that there might be some opportunities, for example, in the small commercial space that could add to the insurer’s already impressive commercial insurance presence.

For now, however, Duperreault said there are no acquisition commitments.

“I can’t tell you we will do one anytime in the near future, but I do look,” Duperreault said. “You can’t find a great [acquisition] if you are not looking, so we do look.”