  In many countries life expectancy gains have been substantially higher than
predicted by even recent forecasts. This is primarily due to increasing rates
of improvement in old-age mortality not captured by existing models. In this
paper we show how the concept of frailty can be used to model both changing
rates of improvement and the deceleration of mortality at old ages, also seen
in data.
  We present a "fragilization" method by which frailty can be added to standard
mortality models. The aim is to improve the modeling and forecasting of old-age
mortality while preserving the structure of the original model and the
underlying stochastic processes. Estimation is based on a general
pseudo-likelihood approach which allows the use of essentially any frailty
distribution and mortality model. We also consider a class of generalized
stochastic frailty models with both frailty and non-frailty terms, and we
describe how these models can be estimated by the EM-algorithm.
  The method is applied to the Lee-Carter model and a parametric time-series
model. For both applications the effect of adding frailty is illustrated with
mortality data for US males.
