in closed form and show that joint presence of both risks leads to over-proportional risk exposure for households. This …

-dependent mortality risk. This is because while a more progressive benefit-earnings rule provides increased insurance for households with … relatively unfavorable earnings histories, and therefore lower savings and survivorship, their relatively high mortality risk …

productivity and aggregate business cycle risk. We show analytically that the whole welfare benefit from joint insurance against … both risks is greater than the sum of benefits from insurance against the isolated risk components. One reason is the … convexity of the welfare gain in total risk. The other reason is a direct risk interaction which amplifies the utility losses …