Some empirical studies firmly reveal that people tend to form overly pessimistic survival expectations for relatively less distant ages and overly optimistic survival expectations for relatively more distant ages. We incorporate this observation into a life-cycle continuous time...

Precautionary saving in response to uninsurable income risk can in principle explain the stylized fact that aggregate saving increases with the variance of income, but it is controversial how much of the observed variation in incomes is, in fact, unpredictable. Borrowing constraints offer an...