The biggest recent weather event was super storm Sandy, which hit the U.S. Northeast at the end of October. Catastrophe modeler Risk Management Solutions said Sandy is expected to ultimately become the second most-costly storm in U.S. history — estimating insured losses as high as $25 billion.
Fishman said, "I don't really know how impactful Sandy will be on prices. Sandy was in the playbook. It was something that all of us in the industry had contemplated."
Last week, Travelers reported better-than-expected fourth-quarter earnings on improvement in underwriting margins. The results do not reflect the full impact of Sandy, he said.
(Read More: Travelers Shares Touch All-Time High After Earnings Beat)
(Read More: Chubb's Q4 Profit Drops on Big Sandy Costs)
Besides the weather, low interest rates have caused Travelers to pass along its costs to customers. "The decline in interest rates, unprecedented, and for an industry that invests in fixed-income securities, it's a cost of what we do. As rates fell, we've got to reflect that in pricing."
America's Debt Crisis
The approach to reining in the U.S. federal deficit shouldn't solely focus on taxes and spending, but also dealing with entitlements, now that the baby boomer generation has started to retire, Travelers CEO Fishman said on CNBC.
"There are 10,000 people a day turning 65 for the next 19 years," he noted. "It's a demographic challenge that we never faced before."
(Read More: Senate Approves Increase in Debt Limit)
Travelers is taking steps to raise awareness about the nation's debt problems. It's partnered with public television to present "Overdraft," which is described as a nonpartisan documentary.
Baby boomers have had an economic impact as they've moved through all the stages of their lives, Fishman said in Friday's interview.
"Social Security, Medicaid and Medicare was a trillion and a half dollars [this past year]," he said. "By 2020, simply because of the demographic shift in the country, that's going to be two and a half trillion dollars." Fishman said that number is equal to all the tax revenue the government took in last year.
As for how he would start to fix the problem, he said, "I would go about it first by aggressively means-testing Social Security. And really driving it to those people that it's supposed to help."
Fishman added that he thinks that entitlement programs have become part of the American fabric. "To have a serious discussion about eliminating them is really silly," he said. "We're not going to do that. So the question is how do you make it work."
—By CNBC's Matthew J. Belvedere; Follow him on Twitter