When Bob Dempsey began shopping for a new home insurance policy last summer, he did not think of his neighborhood as prone to dangerous weather.

His two-story brick home in the Houston suburb of Clear Lake is not directly on the water. In 2017, when Hurricane Harvey unleashed more than 25 inches of rain on the region, Dempsey’s house did not flood. Yet most major insurers turned him down last year. The ones that did offer to sell him a policy — companies he had never heard of — were charging annual premiums between $10,000 and $15,000.