Climate change commitments expose insurers to potential lawsuits if companies fail to live up to their net-zero promises, according to Chubb Ltd. CEO Evan Greenberg.

Speaking during a fireside chat on day two of S&P Global's 38th Annual Insurance Conference, Greenberg said climate change poses a worsening risk to underwriters due not only to more extreme weather but also via lawsuits related to "greenwashing" and net-zero pledges.

Companies that declare themselves to be "net-zero" are going to have to disclose their efforts to shareholders, which Greenberg said poses a challenge to the industry.

"That sounds great in the beginning, but you're going to have to disclose very quickly, all those companies, what's your progress? How are you moving along and achieving that?" Greenberg said. "If it's just vague words, they're going to be a lot of shareholder suits because companies are over-promising."

Greenberg said the problem is worse for insurance companies, which have no way to accurately measure the carbon footprint of their investments and portfolio.

Chubb, as well as society, have competing interests when it comes to climate change, Greenberg added, having obligations to move toward a net-zero emissions world while also supporting energy security in a world that runs on fossil fuels.

Greenberg said Chubb has not declared itself to be a net-zero company because, as an organization, it cannot imagine how to achieve that goal. However, the company is investing in new technologies that will advance carbon neutrality while also continuing to insure gas and oil as the company moves away from coal and tar sands.

Although Chubb has previously restricted underwriting related to the coal industry, in May shareholders rejected a proposal to restrict the underwriting of new fossil fuel supplies.

"We don't yet have great alternatives to gas and oil, and it would be irresponsible of us not to continue to insure those in a responsible way," Greenberg said. "We're trying to develop an ability to underwrite new projects in a scientific-based way where we can determine which ones are done in a more sustainable and responsible way and insure those."