Using data from the Health and Retirement Study linked to administrative Medicare and Medicaid records along with the Medical Expenditure Panel Survey, we estimate the stochastic process for total and out-of-pocket medical spending. By focusing on dynamics, we consider not only the risk of catastrophic expenses in a single year, but also the risk of moderate but persistent expenses that accumulate into a catastrophic lifetime cost. We assess the reduction in out-of-pocket medical spending risk provided by public insurance schemes such as Medicare or Medicaid. We find that although Medicare and Medicaid pay the majority of medical expenses, households at age 65 will incur, on average, $59,000 in out-of-pocket costs with 10% of households incurring more than $121,000 in out-of-pocket expenses over their remaining lives.