Using the widely-cited Lee-Carter mortality model, we quantify aggregate mortality risk as the risk that the average annuitant lives longer than is predicted by the model, and we conclude that annuity business exposes insurance companies to substantial mortality risk. We calculate that a markup...

Defined benefit pension plans have become considerably less common since the early 1980s, while defined contribution plans have spread. Previous research showed that defined benefit plans, with sharp incentives encouraging retirement after a certain point, contributed to the striking postwar...