Some new results about optimal insurance demand under uncertainty

•We propose a new model to analyze how optimal insurance demand responds to the changes of some factors.•The new model includes a background uncertainty risk.•We show that the background uncertainty risk has effects on optimal insurance demand.

The aim of this paper is to investigate the optimal insurance demand of a risk-averse agent who is faced with background uncertainty. The preferences of the agent are represented by two-moment, mean-standard deviation utility functions. By the comparative statics, we find that under the assumption of decreasing absolute risk aversion (DARA), the changes of background uncertainty have effects on optimal insurance demand.