Precautionary insurance demand with state-dependent background risk

This article considers a zero-mean background risk that is uncorrelated with insurable losses, but is not necessarily statistically independent. In particular, the size of the background risk can vary in different insurable-loss states. We show how a prudent individual will buy either more insurance or less insurance than with no background risk, depending on the relative size of the background risk in the loss states vis-a-vis the no-loss states. If we consider two individuals, with one more risk averse than the other, we need to compare the intensities of their precautionary motives, in addition to their measures of risk aversion, before we can determine who buys more insurance coverage in the presence of the state dependent background risk.