"The pricing environment is pretty good," Greenberg said on a conference call. "But ... that is not addressing by itself the fundamental issue.... Like pandemic, cyber has a catastrophe profile to it."
With increasing digital interconnection in the world, the concentrations of exposure were only growing, Greenberg said.
Chubb's underwriting activities are also exposed to systemic risks arising from cyber threats, Greenberg said, adding that the company is beginning to address it.
Greenberg's comments came as the company reported second-quarter results that far exceeded analysts' estimates due in part to sharp increases in premiums.
Chubb's adjusted operating income rose to $3.62 a share, topping the $3.01 that analysts, on average, expected in the latest quarter, according to data from Refinitiv IBES. It compared with a loss of 56 cents a year earlier, during the early stages of the pandemic.
Net income for the quarter was $5.06 a share, compared with a loss of 73 cents a share a year earlier.
Greenberg also said there has been no change in its stance when it comes to mergers and acquisitions (M&As).
"We're disciplined. Money doesn't burn a hole in our pocket," Greenberg said.
Property & casualty net premiums written, a measure of revenue, rose 15.5% to $8.9 billion. Chubb noted a 13.5% rise in P&C premium rates for commercial insurance in North America, and a 16% gain internationally.
"Based on what we see today, I am confident these market conditions will continue,” Greenberg said.