I present a framework to study the evolution of traits that allow an organism to survive life-threatening but rare risks. Specifically, I am concerned with risks so rare that any one individual in a population may not experience the risk-causing event in its lifetime. A theory of rare risk management is virtually absent in evolutionary biology, although it is well developed in economics. This is surprising because of the great influence economics had on evolutionary biology, and because biology is full of examples for evolved risk management traits. They include the ability of bacteria to sporulate, of pathogens to survive antibiotic treatment, of temperate bacteriophages to enter a lytic life cycle, as well as traits that allow higher organisms to survive rare environmental disasters, such as sporadic wildfires and irregular flooding. I make predictions about the sustenance of risk management traits under two scenarios, one where the catastrophic events cause individual deaths, and another one where catastrophic events cause population extinction. A well-developed theory of risk management will not only predict the distribution of risk management traits, but may also serve other purposes, such as to reconstruct the spectrum of environments that an organism encountered in its evolutionary history from the record stored in its genome's memory.