Usikkerhet ved levetidsfremskrivninger

Abstract

In the last hundred years there have been a steady decline in mortality. When we are going to project how mortality is going to be in the future, we need a model who takes this decline in consideration. We have traditionally used a Lee-Carter model with time parameters described by a random walk. The main purpose of this thesis is to find out if we can use an autoregressive model instead.

With data from 1950 to the last available data year in Human Mortality Database (HMD) for Norway, Denmark, Sweden, Japan, France, Italy, Spain, Great Britain and the United States of America, we estimate the time parameters in the Lee-Carter model. When we are looking at the autocorrelation function for the time parameters, we see that they are not independent, but negatively correlated. It's therefore natural to use an autoregressive process with a negative coefficient instead of a random walk when we are estimating the time variables.

To see how well the autoregressive model fits, we use data up to 1997 and Monte Carlo simulations to predict the mortality in 2007. It seems like the autoregressive model is a good fit, but there are some exceptions. Generally it's more difficult to predict the mortality for men than for women.

The consequences of using an autoregressive process instead of a random walk is that we get narrower confidence intervals when we predict mortality. This will again have economic consequences, because narrower confidence intervals gives us less insecurity in our predictions. An insurance company will need less money to have solvency when we use an autoregressive model versus a random walk.