Using the Lee-Carter mortality model, we quantify aggregate mortality risk, the risk that annuitants might live longer than predicted by the model. We calculate that a markup of 4.3 percent on an annuity premium, or else shareholders' capital equal to 4.3 percent of the expected present value of annuity payments, would reduce the probability of insolvency resulting from uncertain aggregate mortality trends to five percent, and a markup of 6.1 percent would reduce the probability of insolvency to one percent. Using the same model, we find evidence that the projection scale that the insurance industry commonly refers to underestimates aggregate mortality improvements. Consequently, annuities that are priced on that projections scale without any conservative margin will be substantially underpriced.Insurance companies could deal with aggregate mortality risk by transferring it to the financial markets through newly-available mortality-contingent bonds. We calculate the returns that investors would have obtained on such bonds had they been available previously, and the historical covariance between these bond returns and the growth in per-capita consumption.Using the Consumption Capital Asset Pricing Model (CCAPM), we determine the risk premium that investors would have required on such bonds. At plausible coefficients of risk aversion, investors should be able to hedge aggregate mortality risk via such bonds at very low cost.

The expectation of needing long-term care is an essential input into optimal saving and long-term care insurance decisions. Previous optimization models have used the Robinson (2002) transition probabilities, which have not been systematically updated and which underpredict the use of care while overpredicting the average stay of people who enter care. We develop a new statistical model and use current data to estimate health impairment and care transition probabilities. We show that impairment and care use have declined and that, after incorporating the new transition probabilities, optimal long-term care insurance holdings are much lower and are close to actual holdings.