This paper shows how the demand for non-life insurance interacts with consumption and saving. The analysis is set in continuous time, using the maximum principle. When insurance is actuarially fair, the insurance and consumption decisions are separable. With loaded premiums, and alternatively without insurance, optimal consumption is dynamically related to the growth rate of the loss probability, and a growing loss probability generates precautionary saving. With loaded premiums, less than full insurance is demanded at each instant, and optimal cover varies over time, whether or not the loss probability is constant.
2004."Insurance, Consumption, and Saving: A Dynamic Analysis in Continuous Time."American Economic Review,
94(4): 1130-1140.DOI: 10.1257/0002828042002642