Shares of the New York insurance giant at last check were up 2.8% to $115.
Travelers reported core profit of $798 million, or $3.12 a share, more than double the $378 million, or $1.43, of the year-earlier quarter. The latest figure exceeded the Zacks consensus estimate of $2.91.
Revenue totaled $8.28 billion, compared with $8.01 billion a year earlier and ahead of Wall Street's call for $8.11 billion.
Consolidated combined ratio improved 6.6 points to 94.9%; underlying combined ratio improved 2.6 points to 91.5%.
Net written premiums increased 3% to $7.77 billion.
Catastrophe losses came to $397 million pretax.
Alan Schnitzer, chairman and chief executive, said in a statement that the company was pleased with the core income "despite catastrophe losses that were well above the 10-year average for the third quarter."
"Our earnings this quarter reflect strong underlying underwriting income, resulting from record quarterly net earned premiums and an underlying combined ratio which improved 2.6 points to 91.5%," Schnitzer said.
Travelers said the catastrophe losses resulted primarily from the derecho windstorm in the U.S. Midwest, the Glass wildfire in California, Tropical Storm Isaias, Hurricane Laura and additional wildfires in the U.S. West.
Net prior-year reserve development also included a $295 million increase to asbestos reserves, compared with a $220 million increase in the prior-year quarter.