The burden of finding health, life, disability and other types of insurance is increasingly falling on individuals. A recently launched online insurance broker PolicyGenius Inc. secured $5.3 million in Series A funds to respond to this trend.

“The insurance and employment-benefits space will be individualized,” said Jennifer Fitzgerald, chief executive and co-founder of Brooklyn, N.Y.-based PolicyGenius. She said that insurance will move the way of pensions, from being offered as a defined benefit by large employers to falling...